Let G be a group and R a set of elements of G with normal closure N. In general, it is not easy to understand the quotient G/N. Small Cancellation Theory is, broadly speaking, a family of conditions of the following form: Let G be a negatively curved group, R a family of ?independent enough? elements. Then G/N is itself negatively curved, and we understand many properties of this quotient. In this talk, I will review the classical Small Cancellation Theory, as well as some of its variants (Graphical Small Cancellation and Geometric Small Cancellation), and exhibit some of the groups with exotic properties that can be constructed using these methods