The importance of autocatalysis spans from practical applications such as in chemically amplified photoresists, to autocatalysis playing a fundamental role in evolution as well as a plausible key role in the origin of life. The phenomenon of autocatalysis is characterized by its kinetic signature rather than by its mechanistic aspects. The molecules that form autocatalytic systems and the mechanisms underlying autocatalytic reactions are very diverse. This chemical diversity, combined with the strong involvement of chemical kinetics, creates a formidable barrier for entrance to the field. Understanding these challenges, we wrote this Review with three main goals in mind: (i) To provide a basic introduction to the kinetics of autocatalytic systems and its relation to the role of autocatalysis in evolution, (ii) To provide a comprehensive overview, including tables, of synthetic chemical autocatalytic systems, and (iii) To provide an in‐depth analysis of the concept of autocatalytic reaction networks, their design, and perspectives for their development.