This book shows how mathematical and computational approaches can be useful to help us understand how killer T-cell responses work to fight viral infections. It also demonstrates that such mathematical and computational approaches are most valuable when coupled with experimental work through collaborations. The interdisciplinary spirit of the research and analysis is reflected in the writing style of the book. While the topic of the book is mathematical modeling, the text is written in such a way that experimental immunologists and virologists without extensive computational background will be able to understand the arguments, and to see the biological implications of theory. The book covers a broad variety of topics, including both basic immunological questions and the application of these insights to the understanding and treatment of pathogenic human diseases.