This article reviews the concepts and methods of Bayesian statistical analysis, which can offer innovative and powerful solutions to some challenging analytical problems that characterize developmental research. In this article, we demonstrate the utility of Bayesian analysis, explain its unique adeptness in some circumstances, address some concerns and misconceptions about the approach, and illustrate some applications of Bayesian analysis to issues that frequently arise in developmental research. The illustrations of the approach provided here reflect several important issues within the domain of moral reasoning development (such as assessing patterns of stage change over time); however, the methods are readily applicable across content areas in developmental research. (Contains 3 figures.)