Shape constraints, motivated by either application-specific assumptions or existing theory, can be imposed during model estimation to restrict the feasible region of the parameters. Although such restrictions may not provide any benefits in an asymptotic analysis, they often improve finite sample performance of statistical estimators and the computational efficiency of finding near-optimal control policies. This paper briefly reviews an illustrative set of research utilizing shape constraints in the economics and operations research literature. We highlight the methodological innovations and applications, with a particular emphasis on utility functions, production economics and sequential decision making applications.