Approximate reasoning has been a very important source of motivations for the development of fuzzy sets and possibility theory. It has also been at the origin of some of the most popular applications of fuzzy set theory. This long chapter is an attempt at providing a coherent view of the abundant body of results published in the field. After restating the necessary background, the paper discusses the representation of different kinds of fuzzy statements, and presents the basic machinery for approximate reasoning based on the combination and projection of possibility distributions. Reasoning with fuzzy rules is especially considered. Then specialized forms of approximate reasoning, such as interpolative reasoning, reasoning about preferences, temporal and qualitative reasoning, are surveyed as well as different fuzzy set-based and possibility theory-based models of plausible reasoning, including similarity-based and case-based reasoning, default reasoning, abductive reasoning, and reasoning with fuzzy quantifiers. The connection between approximate reasoning and certainty factor methods for uncertainty handling is also discussed.