Coloring in a graph refers either to vertex coloring, edge coloring or both in which case it is called total coloring. Each vertex is assigned a color from a set of colors such that no two adjacent vertices have the same color in vertex coloring. Edge coloring is the process of assigning colors to the edges of a graph such that no two edges incident to the same vertex are assigned the same color. We review sequential, parallel, and distributed algorithms for vertex and edge coloring in this chapter.