Submodularity is a property of functions that assign values to subsets of a ground set. It can be characterized by the inequality $f(X) + f(Y) \geq f(X \cap Y) + f(X \cup Y)$. In this talk, we will explain why submodularity is regarded as a discrete equivalent to both convexity and concavity. Furthermore, we will demonstrate some common techniques making use of submodular functions.