diff --git a/crates/bevy_core/src/bytes.rs b/crates/bevy_core/src/bytes.rs
index efcbdf26fb40e..495cc64c41ca3 100644
--- a/crates/bevy_core/src/bytes.rs
+++ b/crates/bevy_core/src/bytes.rs
@@ -231,6 +231,6 @@ mod tests {
 
     #[test]
     fn test_mat4_round_trip() {
-        test_round_trip(Mat4::identity());
+        test_round_trip(Mat4::IDENTITY);
     }
 }
diff --git a/crates/bevy_math/Cargo.toml b/crates/bevy_math/Cargo.toml
index 499a418d81ba4..57dba897ba2f5 100644
--- a/crates/bevy_math/Cargo.toml
+++ b/crates/bevy_math/Cargo.toml
@@ -13,5 +13,5 @@ license = "MIT"
 keywords = ["bevy"]
 
 [dependencies]
-glam = { version = "0.12.0", features = ["serde"] }
+glam = { version = "0.13.0", features = ["serde"] }
 bevy_reflect = { path = "../bevy_reflect", version = "0.4.0", features = ["bevy"] }
diff --git a/crates/bevy_reflect/Cargo.toml b/crates/bevy_reflect/Cargo.toml
index a4f7c9c364f59..6322db13e52fb 100644
--- a/crates/bevy_reflect/Cargo.toml
+++ b/crates/bevy_reflect/Cargo.toml
@@ -30,7 +30,7 @@ parking_lot = "0.11.0"
 thiserror = "1.0"
 serde = "1"
 smallvec = { version = "1.4", features = ["serde"], optional = true }
-glam = { version = "0.12.0", features = ["serde"], optional = true }
+glam = { version = "0.13.0", features = ["serde"], optional = true }
 
 [dev-dependencies]
 ron = "0.6.2"
diff --git a/crates/bevy_render/src/camera/camera.rs b/crates/bevy_render/src/camera/camera.rs
index bebbb39c87675..6f3f694e48db0 100644
--- a/crates/bevy_render/src/camera/camera.rs
+++ b/crates/bevy_render/src/camera/camera.rs
@@ -46,13 +46,13 @@ impl Camera {
         // Build a transform to convert from world to NDC using camera data
         let world_to_ndc: Mat4 =
             self.projection_matrix * camera_transform.compute_matrix().inverse();
-        let ndc_space_coords: Vec3 = world_to_ndc.transform_point3(world_position);
+        let ndc_space_coords: Vec3 = world_to_ndc.project_point3(world_position);
         // NDC z-values outside of 0 < z < 1 are behind the camera and are thus not in screen space
         if ndc_space_coords.z < 0.0 || ndc_space_coords.z > 1.0 {
             return None;
         }
         // Once in NDC space, we can discard the z element and rescale x/y to fit the screen
-        let screen_space_coords = (ndc_space_coords.truncate() + Vec2::one()) / 2.0 * window_size;
+        let screen_space_coords = (ndc_space_coords.truncate() + Vec2::ONE) / 2.0 * window_size;
         Some(screen_space_coords)
     }
 }
diff --git a/crates/bevy_render/src/mesh/shape/torus.rs b/crates/bevy_render/src/mesh/shape/torus.rs
index 830e9738a56a4..e1eedbdeb1e8c 100644
--- a/crates/bevy_render/src/mesh/shape/torus.rs
+++ b/crates/bevy_render/src/mesh/shape/torus.rs
@@ -48,7 +48,7 @@ impl From<Torus> for Mesh {
                 let z = theta.sin() * (torus.radius + torus.ring_radius * phi.cos());
                 let y = torus.ring_radius * phi.sin();
 
-                let normal = segment_pos.cross(Vec3::unit_y()).normalize();
+                let normal = segment_pos.cross(Vec3::Y).normalize();
 
                 positions.push([x, y, z]);
                 normals.push(normal.into());
diff --git a/crates/bevy_text/src/text2d.rs b/crates/bevy_text/src/text2d.rs
index 52b146b843078..c033ea930dde7 100644
--- a/crates/bevy_text/src/text2d.rs
+++ b/crates/bevy_text/src/text2d.rs
@@ -91,14 +91,14 @@ pub fn draw_text2d_system(
         if let Some(text_glyphs) = text_pipeline.get_glyphs(&entity) {
             let position = global_transform.translation
                 + match text.alignment.vertical {
-                    VerticalAlign::Top => Vec3::zero(),
+                    VerticalAlign::Top => Vec3::ZERO,
                     VerticalAlign::Center => Vec3::new(0.0, -height * 0.5, 0.0),
                     VerticalAlign::Bottom => Vec3::new(0.0, -height, 0.0),
                 }
                 + match text.alignment.horizontal {
                     HorizontalAlign::Left => Vec3::new(-width, 0.0, 0.0),
                     HorizontalAlign::Center => Vec3::new(-width * 0.5, 0.0, 0.0),
-                    HorizontalAlign::Right => Vec3::zero(),
+                    HorizontalAlign::Right => Vec3::ZERO,
                 };
 
             let mut drawable_text = DrawableText {
diff --git a/crates/bevy_transform/src/components/global_transform.rs b/crates/bevy_transform/src/components/global_transform.rs
index bb0d5b6105614..63d1c46ae5d2f 100644
--- a/crates/bevy_transform/src/components/global_transform.rs
+++ b/crates/bevy_transform/src/components/global_transform.rs
@@ -21,9 +21,9 @@ impl GlobalTransform {
     #[inline]
     pub fn identity() -> Self {
         GlobalTransform {
-            translation: Vec3::zero(),
-            rotation: Quat::identity(),
-            scale: Vec3::one(),
+            translation: Vec3::ZERO,
+            rotation: Quat::IDENTITY,
+            scale: Vec3::ONE,
         }
     }
 
@@ -77,19 +77,19 @@ impl GlobalTransform {
     #[inline]
     /// Get the unit vector in the local x direction
     pub fn local_x(&self) -> Vec3 {
-        self.rotation * Vec3::unit_x()
+        self.rotation * Vec3::X
     }
 
     #[inline]
     /// Get the unit vector in the local y direction
     pub fn local_y(&self) -> Vec3 {
-        self.rotation * Vec3::unit_y()
+        self.rotation * Vec3::Y
     }
 
     #[inline]
     /// Get the unit vector in the local z direction
     pub fn local_z(&self) -> Vec3 {
-        self.rotation * Vec3::unit_z()
+        self.rotation * Vec3::Z
     }
 
     #[inline]
diff --git a/crates/bevy_transform/src/components/transform.rs b/crates/bevy_transform/src/components/transform.rs
index d09c0bd247c82..3c33d8f0a25fb 100644
--- a/crates/bevy_transform/src/components/transform.rs
+++ b/crates/bevy_transform/src/components/transform.rs
@@ -21,9 +21,9 @@ impl Transform {
     #[inline]
     pub fn identity() -> Self {
         Transform {
-            translation: Vec3::zero(),
-            rotation: Quat::identity(),
-            scale: Vec3::one(),
+            translation: Vec3::ZERO,
+            rotation: Quat::IDENTITY,
+            scale: Vec3::ONE,
         }
     }
 
@@ -77,19 +77,19 @@ impl Transform {
     #[inline]
     /// Get the unit vector in the local x direction
     pub fn local_x(&self) -> Vec3 {
-        self.rotation * Vec3::unit_x()
+        self.rotation * Vec3::X
     }
 
     #[inline]
     /// Get the unit vector in the local y direction
     pub fn local_y(&self) -> Vec3 {
-        self.rotation * Vec3::unit_y()
+        self.rotation * Vec3::Y
     }
 
     #[inline]
     /// Get the unit vector in the local z direction
     pub fn local_z(&self) -> Vec3 {
-        self.rotation * Vec3::unit_z()
+        self.rotation * Vec3::Z
     }
 
     #[inline]
diff --git a/examples/3d/3d_scene.rs b/examples/3d/3d_scene.rs
index 0d90a55ada4bf..e0a5e7cb507ff 100644
--- a/examples/3d/3d_scene.rs
+++ b/examples/3d/3d_scene.rs
@@ -36,8 +36,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(-2.0, 2.5, 5.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(-2.0, 2.5, 5.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/load_gltf.rs b/examples/3d/load_gltf.rs
index de2539c49e6ba..68b5afcc69b37 100644
--- a/examples/3d/load_gltf.rs
+++ b/examples/3d/load_gltf.rs
@@ -17,7 +17,7 @@ fn setup(commands: &mut Commands, asset_server: Res<AssetServer>) {
         })
         .spawn(PerspectiveCameraBundle {
             transform: Transform::from_xyz(0.7, 0.7, 1.0)
-                .looking_at(Vec3::new(0.0, 0.3, 0.0), Vec3::unit_y()),
+                .looking_at(Vec3::new(0.0, 0.3, 0.0), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/msaa.rs b/examples/3d/msaa.rs
index 3df110f66cd16..d32c6745a5286 100644
--- a/examples/3d/msaa.rs
+++ b/examples/3d/msaa.rs
@@ -32,8 +32,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(-3.0, 3.0, 5.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(-3.0, 3.0, 5.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/orthographic.rs b/examples/3d/orthographic.rs
index 82c3ee09d3245..2bf992505ce69 100644
--- a/examples/3d/orthographic.rs
+++ b/examples/3d/orthographic.rs
@@ -17,7 +17,7 @@ fn setup(
     // set up the camera
     let mut camera = OrthographicCameraBundle::new_3d();
     camera.orthographic_projection.scale = 3.0;
-    camera.transform = Transform::from_xyz(5.0, 5.0, 5.0).looking_at(Vec3::zero(), Vec3::unit_y());
+    camera.transform = Transform::from_xyz(5.0, 5.0, 5.0).looking_at(Vec3::ZERO, Vec3::Y);
 
     // add entities to the world
     commands
diff --git a/examples/3d/parenting.rs b/examples/3d/parenting.rs
index 76bc9ec918791..b4613f13236b7 100644
--- a/examples/3d/parenting.rs
+++ b/examples/3d/parenting.rs
@@ -58,8 +58,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(5.0, 10.0, 10.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(5.0, 10.0, 10.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/spawner.rs b/examples/3d/spawner.rs
index 978aaec3663c5..509406e186a53 100644
--- a/examples/3d/spawner.rs
+++ b/examples/3d/spawner.rs
@@ -44,8 +44,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(0.0, 15.0, 150.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(0.0, 15.0, 150.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 
diff --git a/examples/3d/texture.rs b/examples/3d/texture.rs
index 32d0a929d9073..93d46b6484f30 100644
--- a/examples/3d/texture.rs
+++ b/examples/3d/texture.rs
@@ -96,8 +96,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(3.0, 5.0, 8.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(3.0, 5.0, 8.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/update_gltf_scene.rs b/examples/3d/update_gltf_scene.rs
index e8d37707fcf2e..664b16db576df 100644
--- a/examples/3d/update_gltf_scene.rs
+++ b/examples/3d/update_gltf_scene.rs
@@ -31,7 +31,7 @@ fn setup(
         })
         .spawn(PerspectiveCameraBundle {
             transform: Transform::from_xyz(1.05, 0.9, 1.5)
-                .looking_at(Vec3::new(0.0, 0.3, 0.0), Vec3::unit_y()),
+                .looking_at(Vec3::new(0.0, 0.3, 0.0), Vec3::Y),
             ..Default::default()
         });
 
diff --git a/examples/3d/wireframe.rs b/examples/3d/wireframe.rs
index 51e9e8c292014..0737afdb69ce0 100644
--- a/examples/3d/wireframe.rs
+++ b/examples/3d/wireframe.rs
@@ -52,8 +52,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(-2.0, 2.5, 5.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(-2.0, 2.5, 5.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/3d/z_sort_debug.rs b/examples/3d/z_sort_debug.rs
index dc72199bba8de..1faa4ceb419c4 100644
--- a/examples/3d/z_sort_debug.rs
+++ b/examples/3d/z_sort_debug.rs
@@ -83,8 +83,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(5.0, 10.0, 10.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(5.0, 10.0, 10.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/android/android.rs b/examples/android/android.rs
index 51af3e855bd6b..c3eec9d677e24 100644
--- a/examples/android/android.rs
+++ b/examples/android/android.rs
@@ -38,8 +38,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(-2.0, 2.5, 5.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(-2.0, 2.5, 5.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/asset/asset_loading.rs b/examples/asset/asset_loading.rs
index 3f8407ca6a5ca..d4d88c0276d29 100644
--- a/examples/asset/asset_loading.rs
+++ b/examples/asset/asset_loading.rs
@@ -71,8 +71,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(0.0, 3.0, 10.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(0.0, 3.0, 10.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/asset/hot_asset_reloading.rs b/examples/asset/hot_asset_reloading.rs
index b27ba6de82106..05fe82e893493 100644
--- a/examples/asset/hot_asset_reloading.rs
+++ b/examples/asset/hot_asset_reloading.rs
@@ -31,8 +31,7 @@ fn setup(commands: &mut Commands, asset_server: Res<AssetServer>) {
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(2.0, 2.0, 6.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(2.0, 2.0, 6.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/game/alien_cake_addict.rs b/examples/game/alien_cake_addict.rs
index dfa34bd448a18..9885efeb20b71 100644
--- a/examples/game/alien_cake_addict.rs
+++ b/examples/game/alien_cake_addict.rs
@@ -109,7 +109,7 @@ fn setup_cameras(commands: &mut Commands, mut game: ResMut<Game>) {
                 2.0 * BOARD_SIZE_J as f32 / 3.0,
                 BOARD_SIZE_J as f32 / 2.0 - 0.5,
             )
-            .looking_at(game.camera_is_focus, Vec3::unit_y()),
+            .looking_at(game.camera_is_focus, Vec3::Y),
             ..Default::default()
         })
         .spawn(UiCameraBundle::default());
@@ -301,7 +301,7 @@ fn focus_camera(
     // look at that new camera's actual focus
     for (mut transform, camera) in transforms.q0_mut().iter_mut() {
         if camera.name == Some(CAMERA_3D.to_string()) {
-            *transform = transform.looking_at(game.camera_is_focus, Vec3::unit_y());
+            *transform = transform.looking_at(game.camera_is_focus, Vec3::Y);
         }
     }
 }
diff --git a/examples/ios/src/lib.rs b/examples/ios/src/lib.rs
index cbc8fe9b2ca1a..983f2d759044b 100644
--- a/examples/ios/src/lib.rs
+++ b/examples/ios/src/lib.rs
@@ -53,8 +53,7 @@ fn setup(
         })
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(-2.0, 2.5, 5.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(-2.0, 2.5, 5.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/shader/array_texture.rs b/examples/shader/array_texture.rs
index 43912ab0853fb..a58621b2eaaa2 100644
--- a/examples/shader/array_texture.rs
+++ b/examples/shader/array_texture.rs
@@ -110,7 +110,7 @@ fn setup(
         .unwrap();
 
     commands.spawn(PerspectiveCameraBundle {
-        transform: Transform::from_xyz(2.0, 2.0, 2.0).looking_at(Vec3::default(), Vec3::unit_y()),
+        transform: Transform::from_xyz(2.0, 2.0, 2.0).looking_at(Vec3::default(), Vec3::Y),
         ..Default::default()
     });
 }
diff --git a/examples/shader/hot_shader_reloading.rs b/examples/shader/hot_shader_reloading.rs
index 6f675224a4a9e..a12a25acd85a8 100644
--- a/examples/shader/hot_shader_reloading.rs
+++ b/examples/shader/hot_shader_reloading.rs
@@ -73,8 +73,7 @@ fn setup(
         .with(material)
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(3.0, 5.0, -8.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(3.0, 5.0, -8.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/shader/mesh_custom_attribute.rs b/examples/shader/mesh_custom_attribute.rs
index 6d0d2ca09e295..778325acded01 100644
--- a/examples/shader/mesh_custom_attribute.rs
+++ b/examples/shader/mesh_custom_attribute.rs
@@ -138,8 +138,7 @@ fn setup(
         .with(material)
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(3.0, 5.0, -8.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(3.0, 5.0, -8.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/shader/shader_custom_material.rs b/examples/shader/shader_custom_material.rs
index dc02029f37709..0c25563306f8f 100644
--- a/examples/shader/shader_custom_material.rs
+++ b/examples/shader/shader_custom_material.rs
@@ -94,8 +94,7 @@ fn setup(
         .with(material)
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(3.0, 5.0, -8.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(3.0, 5.0, -8.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/shader/shader_defs.rs b/examples/shader/shader_defs.rs
index 383ffd04e2229..25d131bac38f7 100644
--- a/examples/shader/shader_defs.rs
+++ b/examples/shader/shader_defs.rs
@@ -125,8 +125,7 @@ fn setup(
         .with(blue_material)
         // camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(3.0, 5.0, -8.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(3.0, 5.0, -8.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }
diff --git a/examples/window/multiple_windows.rs b/examples/window/multiple_windows.rs
index 34c868f128734..29fa869930b7f 100644
--- a/examples/window/multiple_windows.rs
+++ b/examples/window/multiple_windows.rs
@@ -190,8 +190,7 @@ fn setup_pipeline(
         })
         // main camera
         .spawn(PerspectiveCameraBundle {
-            transform: Transform::from_xyz(0.0, 0.0, 6.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(0.0, 0.0, 6.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         })
         // second window camera
@@ -201,8 +200,7 @@ fn setup_pipeline(
                 window: window_id,
                 ..Default::default()
             },
-            transform: Transform::from_xyz(6.0, 0.0, 0.0)
-                .looking_at(Vec3::default(), Vec3::unit_y()),
+            transform: Transform::from_xyz(6.0, 0.0, 0.0).looking_at(Vec3::default(), Vec3::Y),
             ..Default::default()
         });
 }