Rivers are amazing sculptors of land. Over eons of time, waterways, both large and small, are responsible for much of what is observable about the landscape. The fact that water runs downhill is well known, but the way rivers shape the land is much more interesting than just simple higher-to-lower progressions.
There are three major factors involved in how rivers make changes to the land through which they travel: erosion, transportation, and deposition. Erosion is well known for the fact that water will scour land, as long as it is soft enough, by passing over it. Transportation occurs when rock materials are moved by a river by actual force, by breaking into pieces and by being suspended in water. Deposition means that the water can also drop, or deposit, the soil or rock materials it carries. An additional factor that contributes to changes in the land is called weathering which consists primarily of freeze-thaw cycles breaking rocks into pieces, chemical weathering from the acid in rain, and the actions of animals which disturb soil and rocks. The final factor in changing the land around a river is gravity; broken rocks roll downhill toward the river bed, deepening the channel of the river.
All rivers can be roughly divided into three stages or courses. The upper course includes the source, the place from which the trickle or stream originates. Because this is at higher elevation than the eventual mouth of the river where it ends, the upper course erodes in a V shape and forms a deep, narrow valley. The upper course will flow through softer soil and rock formations but will veer aside around harder rock forming outcroppings or spurs. Because these alternate with unobstructed areas of flow, these are called interlocking spurs and can be observed as rivers and streams make their way down mountainsides. They look a little like zipper teeth. Where the river encounters rock so hard it cannot erode with softer rock underneath, it will drop over and form a waterfall.
The middle course of a river reaches somewhat flatter places where its rate of speed varies enough that the rate of erosion will vary from one side to another. Where the water moves faster, more erosion occurs and the bank of the river will bend outward and eventually become a steep cliff. Opposite that bank, flow of the river slows enough that it begins to deposit its sand, soil, and rocks to form an entirely different, flatter kind of bank like a sandbank. This creates curves in a river called oxbow lake.
The lower course of a river is mainly occupied with depositing its load of soils, sands, and dissolved solids because it usually flows more slowly over a wider path until it reaches its destination which will be a lake or the ocean. A very large river with heavy deposits will move so slowly that it will form a delta, a new land mass made of the rich soils the river has carried from upstream. Within a delta, new riverbeds will be forced to form so that the water can eventually reach the lake or sea where it is called the mouth of the river.