Synchronization, epidemic processes and information spread are natural processes that emerge from the interaction between people. Mathematically, all of them can be described by models that, despite being simple, are able to predict collective behavior. Furthermore, they share a very interesting feature in common: a phase transition from a so-called active state to an absorbing state. In this presentation, we will show the analytical and computational approaches used to investigate these classic models of statistical physics that present phase transitions in complex networks and we will also show how the network topology influences such dynamic processes. The behavior of such dynamics can be much richer than we previously thought.