We make the case that psychologists should make wider use of structural econometric methods. These methods involve the development of maximum likelihood estimates of models, where the likelihood function is tailored to the structural model. In recent years these models have been developed for a wide range of behavioral models of choice under uncertainty. We explain the components of this methodology, and illustrate with applications to major models from psychology. The goal is to build, and traverse, a constructive bridge between the modeling insights of psychology and the statistical tools of economists.