Producers and consumers of test scores are increasingly concerned about fraudulent behavior before and during the test. There exist several statistical or psychometric methods for detecting fraudulent behavior on tests. This paper provides a review of the Bayesian approaches among them. Four hitherto-unpublished real data examples are provided to demonstrate the application of Bayesian approaches to detect various types of fraudulent behavior on tests. The examples show that Bayesian methods can be useful in detecting several types of test fraud. [This paper was published in "Measurement: Interdisciplinary Research and Perspectives" (EJ1174692).]