The Bayes factor has a basic and crucial role in Bayesian evaluation of psychological hypotheses and models. It forms a fundamental part of the advancement of psychological science. Its computation has been a major challenge, although recent advances in numerical estimation methods such as bridge sampling may allow the application of the Bayes factor to a wide range of practical research contexts. The objective of the current paper is to provide psychological scientists an introductory tutorial of the ideas and recent developments concerning the Bayes factor. Some running examples are presented and a few practical application methods are also discussed.