Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets, and autopoietic systems.