In statistical physics the emergence of large scale collective phenomena out of local interactions between simple agents takes place in general only for very special (zero measure) / critical values of the parameters (temperature, pressure, etc).
Yet in nature collective objects and their large scale dynamics are ubiquitous features dominating our daily experience.
Each of the last decades proposed a different generic mechanism for the emergence of macroscopic complex dynamics out of local microscopic laws.
Nowadays it seems that most of the instances in which microscopic events are promoted to macroscopic changes are related to some form of autocatalytic process.
Identifying the relevant autocatalytic process allows one to gain understanding and control on the seemingly messy empirical systems.
I will review some of the instances in which the resulting models were analytically tractable and in which the theoretical predictions were confirmed by the data.