Chapter 5 takes the approach that the Bayesian, empirical Bayesian and frequentist methods are useful and that in general there should not be much disagreement between the scientific conclusions that are drawn in the practical setting. This chapter provides a basic introduction to the Bayesian view on statistical testing strategies. In this chapter, we focus on basic scenarios of testing that can be easily extended to more complicated situations of statistical decision-making procedures. We show an optimality property relative to using Bayes factor statistics. Chapter 5 introduces considerations of the relevant computational aspects, asymptotic approximations, prior selection issues and provides brief illustrations and some remarks regarding a relationship between Bayesian (Baes factor) and frequentist ( p-values ) strategies for statistical testing.