Asynchronous design has been an active area of research since at least the mid 1950's, but has yet to achieve widespread use. We examine the benefits and problems inherent in asynchronous computations, and in some of the more notable design methodologies. These include Huffman asynchronous circuits, burst-mode circuits, micropipelines, template-based and trace theory-based delay-insensitive circuits, signal transition graphs, change diagrams, and compilation-based quasidelay-insensitive circuits.