The Wodarz lab works on mathematical and computational models of biological processes, with an emphasis on biomedical applications. Evolutionary dynamics is a unifying theme across different areas of investigation. These include the following: (i) Dynamics of cancer and its treatment. Mathematical models are developed that describe the clonal evolution of cells in healthy tissue, the growth and evolution of cancer cells during carcinogenesis, and the response of cancers to therapies. This includes modeling resistance evolution, and how resistance-induced treatment failure can be prevented. Recent research has focused particularly on the hematopoietic system and on hematopoietic malignancies, but has also included a number of solid tumors. One of the goals of this work is to use the mathematical models to develop patient-specific predictions of treatment outcomes, by applying models to clinical data through collaborations. (ii) Dynamics of virus infections and immune responses. Mathematical models are developed that describe the complex interactions between in vivo virus spread and anti-viral immune responses. A long-standing interest has been the interactions between viral infections and cytotoxic T lymphocyte (CTL) responses, particularly in the context of human immunodeficiency virus (HIV), and experimental mouse infections. The goal is to better understand correlates of CTL-mediated virus control, to study how virus evolution can influence the course of disease, and to analyze treatment interventions to improve virus control in the context of evolving virus populations. (iii) Evolutionary theory. Evolutionary processes are a recurrent theme in the biomedical applications. To complement this work, new evolutionary theory is developed. Particular emphasis is placed on the role of spatially restricted population growth on evolutionary outcomes, such as the emergence of different kinds of mutants or the crossing of fitness valleys. More generally, the goal is to understand how assumptions about population structure influence evolutionary dynamics, with special relevance to bacterial and eukaryotic cell populations.