There has been an explosion of work recently concerning the development of default Bayesian methods of model selection and hypothesis testing. The four most studied approaches have been the Conventional Prior approach, the Bayes Information Criterion, the Intrinsic Bayes Factor, and the Fractional Bayes Factor. This paper is devoted to discussion and comparison of these four methods. (Certain more recent, and less studied, methods will also be mentioned, as appropriate.) Since our conclusion will be that all four methods have value and should be part of the future Bayesian toolkit, the discussion will focus on general guidelines as to when each is appropriate or inappropriate. Postscript File (689kB)