They were formed about 80 to 55 million years ago when North America started breaking up from Pangaea. As a result, tectonic plates slid under the North American plate. Since the angle of subduction was shallow, there was a broad belt of Mountains along the Western side of North America. Since then, further tectonic activity and glaciers have carved the mountains into peaks and valleys.
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There's also faults and folding.
There are two types of dip slip faults: normal and reverse. The normal fault is when the hanging wall has moved downward off the footwall. They happen when two blocks of rock are pulled apart. Reverse faults are the opposite of normal faults. If the hanging wall rises up the footwall, you have a reverse fault. Also, they occur in areas with compression. A strike slip fault is a type of fault where two blocks of land move horizontally instead of vertically. They form between two small blocks of land, plates of the crust or sometimes continental plates.
Erosion and weathering also play an important role to mountains. In a million years, I predict that the mountains will be much rounder. I base this from the fact that older mountains are rounder while newer ones are much more pointy.