  Some stochastic systems are particularly interesting as they exhibit critical
behavior without fine-tuning of a parameter, a phenomenon called self-organized
criticality. In the context of driven-dissipative steady states, one of the
main models is that of Activated Random Walks. Long-range effects intrinsic to
the conservative dynamics and lack of a simple algebraic structure cause
standard tools and techniques to break down. This makes the mathematical study
of this model remarkably challenging. Yet, some exciting progress has been made
in the last ten years, with the development of a framework of tools and methods
which is finally becoming more structured. In these lecture notes we present
the existing results and reproduce the techniques developed so far.
