Mixed-effects models have found broad applications in various fields. As a result, the interest in learning and using these models is rapidly growing. On the other hand, some of these models, such as the linear mixed models and generalized linear mixed models, are highly parametric, involving distributional assumptions that may not be satisfied in real-life problems. Therefore, it is important, from a practical standpoint, that the methods of inference about these models are robust to violation of model assumptions. Fortunately, there is a full scale of methods currently available that are robust in certain aspects. Learning about these methods is essential for the practice of mixed-effects models. This research monograph provides a comprehensive account of methods of mixed model analysis that are robust in various aspects, such as violation of model assumptions, or to outliers. It is also suitable as a reference book for a practitioner who uses the mixed-effects models, a researcher who studies these models, or as a graduate text for a course on mixed-effects models and their applications.