This chapter deals with nonlinear scalarization functions, considered in vector optimization/set optimization, in the setting of general vector spaces with or without any topology on the acting space equipped with a constant cone, variable domination structures or general preferences. We study a nonlinear scalarization function with respect to certain set order relations induced by the domination set. We provide several properties of such a scalarization function by using algebraic notions such as vector closure and algebraic interior. We study the relations among different kinds of optimal elements of a family of subsets of a general vector space by means of variable domination structures. We obtain several characterizations for different kinds of optimal elements of a family of sets by means of nonlinear scalarization functions. We provide an application to vector-valued games with uncertainty.