One of the major areas in combinatorics is extremal combinatorics. The fundamental questions consist in determining the maximum size of a family of objects which does not contain a prescribed configuration. For example, the Turan problem involves the determination of the maximum number of edges in a graph containing no copies of a prescribed subgraph. In this talk, I will discuss some simple extremal problems for families of sets, some recent advances in the field, as well as few of the connections to other branches of mathematics.