A River god, or Potamus, is a nature spirit that presides over a river. Each river has a god, that are sons of Oceanus. Their daughters are the fresh water naiads and their appearance is often not completely human, with animal features.
Potamoi are the sons of the water Titans Oceanus and Tethys, and are brothers of the Oceanids, also children of Oceanus. Every river has an eponymous river god. Potamoi often have many daughters, the naiads, who inhabit the river or a nearby body of water.
The Underworld rivers are a little different, having magical properties. The River Styx is a nymph, the first-born of Oceanus who fought on the side of the Olympians in the First Titan War along with her children, including Nike. She is also known as the goddess of hatred and oaths sworn by her waters is binding, even to the gods. The River Lethe which causes memory loss is also a goddess, while the River Phlegethon made of fire, the River Cocytus of lamentation, and the River Acheron of pain are gods.
As water spirits, Potamoi can change their shape and thus can appear anyway they want. They often appear either as human or partly human. In mythology, they can appear fully human or partly fish- and/or bull-like, for example Achelous who is a man-headed bull. The East River Spirit resembles a Telekhine, partly wolf- and seal-like, whereas The Hudson River Spirit and Tiberinus appear human.
Additionally, being nature spirits they reflect the state of their river. A common problem is pollution. The East River is said to have radioactive green eyes, and the Hudson River wears chain-mail made of trash. Tiberinus is said to wear a lot of cologne, probably to mask the smell of the Tiber.