The list chromatic number of a graph G is the minimum k so that for every assignment of a list of k colors to any vertex of G there is a proper vertex coloring assigning to each vertex a color from its list. This notion was introduced by Vizing and by Erdos, Rubin and Taylor in the late 70s and its study combines combinatorial, probabilistic and algebraic techniques. I will describe some of the contribution of Benny Sudakov to the subject and discuss several old and several new problems and results in the area.