Coagulation equations are models of cluster growth based on the mass action law of chemical kinetics. They occur very often in the scientic literature (in Chemistry, Colloidal Science, Physics, Astrophysics, etc.) and its mathematical study has seen re- markable advances in the last quarter century. One of the current active research topics in this area is the investigation of self-similar behaviour of solutions. In this talk I will provide a gentle introduction to these problems, presenting some of the known results and current open problems.