The Grand Canyon of the Yellowstone

The Grand Canyon of the Yellowstone is one of the greatest sights in Yellowstone National Park. It's also a great example of a canyon.
Canyons don't form everywhere, only in places where a river is cutting downward much faster than the rocks it cuts are weathering. That creates a deep valley with steep, rocky sides. Here, the Yellowstone River is strongly erosive because it carries a lot of water at a steep gradient down from the high, uplifted plateau around the huge Yellowstone caldera. As it cuts its way downward, the sides of the canyon fall into it and are carried away.
The famous yellow rocks here are thick deposits of welded volcanic ash, built up as the Yellowstone hot spot has torched its way through the North American crustal plate. The hot spot is not dead, only resting between eruptions.