The purpose of this essay is to overview of some of the most important results stemming from this contemporary research. The topics reviewed in each section of this essay are as follows: Section 1 gives motivating examples which illustrate a variety of ways in which the actions of agents depend crucially upon their having, or lacking, certain common knowledge. Section 2 discusses alternative analyses of common knowledge. Section 3 reviews applications of multi-agent knowledge concepts, particularly to game theory (von Neumann and Morgenstern 1944), in which common knowledge assumptions have been found to have great importance in justifying solution concepts for mathematical games. Section 4 discusses skeptical doubts about the attainability of common knowledge. Finally, Section 5 discusses the common belief concept which result from weakening the assumptions of Lewis' account of common knowledge.