In this chapter a very wide class of statistical tests based on the empirical distribution function (EDF) is introduced. Among these tests we find some old tests, as the Kolmogorov-Smirnov test, but also in recent years new tests have still been added to this class. A discussion on the EDF and empirical processes has been given in Sections 2.1 and 2.2. Sections 5.1 and 5.2 are devoted to the Kolmogorov-Smirnov and the Cramer-von Mises type tests, respectively. In Section 5.3 we generate the class of EDF tests so that also more recent tests based on the empirical quantile function or the empirical characteristic function fit into the framework. We show that many of these tests are closely related to the class of smooth tests. Practical guidelines are provided in Section 5.6.