Convex functions are defined through the convexity of their epigraphs (subsets of \(H\times {\textsf{R}\!\!\!|}\) ). Their geometric structure, in association with the separation theorems on convex sets, gives birth to the theory of convex functions (continuity, differentiability, ...) and to the development of convex programming (minimization of a convex function over a convex set). In contrast, quasiconvex functions are defined through the convexity of their lower level sets (subsets of H). Despite this loss of one dimension, some (much) of the rich properties induced by the convexity of epigraphs are preserved when epigraphs are replaced by lower level sets. The first object of this chapter is to provide an introduction to quasiconvex and pseudoconvex functions and their applications to optimization and economics. The second object is devoted to generalized monotonicity and variational inequalities. Indeed, thanks to Kuhn-Tucker conditions, the optimal set of the minimization of a (pseudo) convex function over a convex set can be described via (pseudo) monotone variational inequalities. In case of differentiable functions, the gradients of quasi/pseudoconvex functions are quasi/pseudo monotone. But there are generalized monotone variational inequalities which cannot be associated with optimization problems. Complementarity problems are part of variational inequalities, there are discussed in the chapter.