This book presents an alternative for traditional null hypothesis testing. It builds on the idea that researchers usually have more informative research-questions than the "nothing is going on" null hypothesis, or the "something is going on" alternative hypothesis. To be more precise, researchers often express their expectations in terms of expected orderings in parameters, for instance, in group means. This book introduces a novel approach, wherein theories or expectations of empirical researchers are translated into one or more so-called informative hypotheses, i.e., hypotheses imposing inequality constraints on (some of) the model parameters. As a consequence, informative hypotheses are much closer to the actual questions researchers have and therefore make optimal use of the data to provide more informative answers to these questions. A Bayesian approach is used for the evaluation of informative hypotheses and is introduced at a non-technical level in the context of analysis of variance models. Technical aspects of Bayesian evaluation of informative hypotheses are also considered and different approaches are presented by an international group of Bayesian statisticians. Furthermore, applications in a variety of statistical models including among others latent class analysis and multi-level modeling are presented, again at a non-technical level. Finally, the proposed method is evaluated from a psychological, statistical and philosophical point of view. This book contains numerous illustrations, all in the context of psychology. The proposed methodology, however, is equally relevant for research in other social sciences (e.g., sociology or educational sciences), as well as in other disciplines (e.g., medical or economical research). The editors are all affiliated at the faculty of Social Sciences at Utrecht University in the Netherlands. Herbert Hoijtink is a professor in applied Bayesian statistics at the Department of Methodology and Statistics. Irene Klugkist is assistant professor at the same department, and Paul A. Boelen is assistant professor at the Department of Clinical and Health Psychology.