The purpose of this talk is to offer a brief introduction into set-valued and variational analysis and to try to motivate the study of this area. To this end, we first discuss some basic notions and ideas. Namely, we try to explain why set-valued mappings should be analyzed, what properties of such mappings seem to be useful and are typically studied, as well as how one can analyze them, i.e., what are the available tools. It should not be very surprising that, just like in the standard analysis of functions, derivatives play a crucial role. Thus, we clarify how to differentiate set-valued mappings using the machinery of variational geometry (tangent and normal cones). Then we discuss in more depth the topic of calculus rules that enable one to properly manipulate with generalized derivatives and apply them to practically relevant problems. We conclude with some remarks about the new property of semismoothness* for set-valued mappings and the related Newton method for solving generalized equations (inclusions).