In this chapter we will apply the idea of the Direct Method to minimization problems settled on the space of Lipschitz continuous functions. Thus, rather than seeking a minimizer in a Sobolev space, we will settle the problem over a space of Lipschitz functions. The chapter is mostly focused on the so-called Bounded Slope Condition, which permits to infer existence of Lipschitz minimizers, under fairly general assumption on the convex functional to be minimized. In particular, we can allow for variational integrals including the remarkable area functional, which was excluded from the theory developed in Chap. 4 . Some examples and counter-examples complement the chapter.