The prevailing type of fish locomotion is swimming in water. In addition, some fish can "walk", i.e., move over land, burrow in mud, and glide through the air.
Fish swim by exerting force against the surrounding water. There are exceptions, but this is normally achieved by the fish contracting muscles on either side of its body in order to generate waves of flexion that travel the length of the body from nose to tail, generally getting larger as they go along. The vector forces exerted on the water by such motion cancel out laterally, but generate a net force backwards which in turn pushes the fish forward through the water.
Most fishes generate thrust using lateral movements of their body & caudal fin. But there are also a huge number of species that move mainly using their median and paired fins. The latter group profits from the gained manoeuvrability that is needed when living in coral reefs for example. But they can't swim as fast as fish using their bodies & caudal fins.
There are five groups that differ in the fraction of their body that is displaced laterally [1]:
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