This chapter provides an overview of a large class of artificial chemistries, formal rewriting systems. A brief introduction explains the general concept of rewriting or production systems. We then explore the classical lambda calculus which was used as an early example of an AC. Further sections are devoted to an AC computer language, Gamma, and the chemical abstract machine formalism. Other examples of ACs follow, among them the chemical rewriting system on multisets, P systems, and MGS. The chapter concludes with a short discussion of other formal calculi inspired by a chemical metaphor and an explanation of how L systems and other rewriting systems would fit into the category of Artificial Chemistries.