Rivers begin high up in the mountains so they flow quickly downhill eroding the landscape vertically.
The river cuts a deep notch down into the landscape using hydraulic action, when the sheer force of the water gets into small cracks and breaks down the sides of the river valley. Corrasion (abrasion) also occurs which is when the river bed and banks are eroded by the load hitting against them. Another type of erosion that happens is corrosion (solution), when the river water dissolves minerals from the rocks and washes them away.
As the river erodes downwards the sides of the valley are exposed to freeze-thaw weathering which loosens the rocks (some of which will fall into the river) and steepens the valley sides.
The rocks which have fallen into the river assist the process of corrasion and this leads to further erosion.
The river transports the rocks downstream and the channel becomes wider and deeper creating a V-shaped valley between interlocking spurs.