The chemistry that occurs in interstellar clouds consists of both gas-phase processes and reactions on the surfaces of dust grains, the latter particularly on and in water-dominated ice mantles in cold clouds. Some of these processes, especially at low temperature, are very unusual by terrestrial standards. For example, in the gas-phase, two-body association reactions form a metastable species known as a complex, which is then stabilized by the emission of radiation under low-density conditions, especially at low temperatures. In the solid phase, it has been thought that the major process for surface reactions is diffusive in nature, occurring when two species undergoing random walks collide with each other on a surface that has both potential wells and intermediate barriers. There is experimental evidence for this process, although very few rates at low interstellar temperatures are well measured. Moreover, since dust particles are discrete, modeling has to take account that reactant pairs are on the same grain, a problem that can be treated using stochastic approaches. In addition, it has been shown more recently that surface reactions can occur more rapidly if they undergo any of a number of non-diffusive processes including so-called three-body mechanisms. There is some experimental support for this hypothesis. These and other unusual gaseous and solid-state processes will be discussed from the theoretical and experimental points of view, and their possible role in the synthesis of organic molecules in interstellar clouds explained. In addition, their historical development will be reviewed.