General Circulation Models (GCM) have become the most important tool for climate modelers. However, due to their increased complexity, statistical validation of GCM output has become challenging. This study gives an overview of the most widely used statistical techniques in the climate modeling community. Assumptions for each test are verified for typical GCM output examples. The most pertinent problems brought up by the community are addressed. Both classical tests and modern non-parametric tests are investigated for both regime changes (changes of mean) and changes in variability (variance around the mean). Finally, the performance of each test is analyzed in order to give the reader a clear view on which test to use for a particular case.