A phase transition can be understood as the sudden change of the properties of a system with only a small change in conditions. Whether it's the freezing of water, a nuclear reactor reaching its critical point, or the extinction of a pandemic, all these events depend on phenomena related to phase transitions.

In this talk, we step into the world of phase transitions from a probabilistic perspective. Our focus will be percolation, the simplest model in statistical physics to observe a non-trivial phase transition. The talk will be an accessible tour of the main results related to percolation and the beautiful techniques that have been built to understand its critical phenomena.