  The goal of cancer immunotherapy is to boost a patient's immune response to a
tumor. Yet, the design of an effective immunotherapy is complicated by various
factors, including a potentially immunosuppressive tumor microenvironment,
immune-modulating effects of conventional treatments, and therapy-related
toxicities. These complexities can be incorporated into mathematical and
computational models of cancer immunotherapy that can then be used to aid in
rational therapy design. In this review, we survey modeling approaches under
the umbrella of the major challenges facing immunotherapy development, which
encompass tumor classification, optimal treatment scheduling, and combination
therapy design. Although overlapping, each challenge has presented unique
opportunities for modelers to make contributions using analytical and numerical
analysis of model outcomes, as well as optimization algorithms. We discuss
several examples of models that have grown in complexity as more biological
information has become available, showcasing how model development is a dynamic
process interlinked with the rapid advances in tumor-immune biology. We
conclude the review with recommendations for modelers both with respect to
methodology and biological direction that might help keep modelers at the
forefront of cancer immunotherapy development.
