Random or stochastic equations appear frequently in the mathematical description of phenomena in the biological, engineering, and physical sciences. The manner in which these equations arise is elucidated and several important applications of stochastic integral equations of the Volterra type in the engineering and biological sciences are presented in order to acquaint the reader with the importance of stochastic equations and how they are used in physical situations. Included in these applications are problems in control theory, statistical turbulence, and telephone traffic theory. Two biological problems, one concerning a mathematical model for chemotherapy and the other concerning population growth, which have been treated previously us deterministic integral equations, are presenter in a more realistic stochastic framework.