Residual analysis has long been an effective tool for evaluating earthquake forecast models. In this thesis, we not only present simple numerical summaries, but also focus on graphical residual methods including pixel-based approaches, Voronoi methods and super-thinned residuals. Competing models in the Collaboratory for the Study of Earthquake Predictability (CSEP) are evaluated and compared using the residual analysis techniques, and the goodness-of-fit and deficiencies are assessed for each model.