This talk will review results in Zellner (1994, 1995 and 1996) and papers by Green and Strawderman, Currie and Zellner and Sacks and then take up my recent joint work with Justin Tobias. It will be shown how predictive densities produced by various approaches, e.g. BMOM, traditional Bayes, etc. can be compared and/or combined using posterior odds and other model selection procedures. As will be seen, different approaches involve different assumptions and hence lead to different post-data densities for parameters and different predictive densities. Using data and appropriate model selection procedures to choose among alternative models appears to be an appropriate procedure for iterating in on a model that works well in practice.