Immunotherapy has revolutionized cancer treatment by delivering durable remission outcomes to many cancer patients in recent years. T-cell immunotherapy relies on enhancing or replacing immune cells, which can recognize and eliminate a growing malignancy in much the same way as infected cells are cleared during an infection. While promising, this strategy does not eliminate cancer in all patients. The fundamental dynamics of the cancer-immune interaction are quite complex owing in part to a large number of unique T-cell clones and significant intra-tumor heterogeneity. To-date, most of the understanding and principles underlying immunotherapy have been driven empirically. It is this complexity, together with the future benefit of improved clinical outcomes, that makes studying the cancer-immune interaction an ideal applied mathematics problem. I sought to create several foundational mathematical models of the interplay between a continuously adaptive immune system and an evolving cancer population that may evade immune recognition. By applying stochastic process theory to this problem, I generated a framework for addressing various questions related to cancer detection, recognition, and evasion. I first studied the effects of thymic negative selection on T-cell recognition of tumor-associated antigens, which are detectable peptide fragments that closely resemble self-peptide. I quantified the detection of near-self peptide relative to a completely random peptide, predicting that thymic selection minimally affects their recognition. I then studied the temporal dynamics of a population of cancer cells which may evolve mechanisms of immune evasion. My foundational model predicts variations in immunotherapeutic efficacy as a function of immune-relevant parameters and tracks the population-level behavior of an evolving threat under adaptive immune recognition. I end by proposing a framework for threats like cancer which optimize their evasion rate in order to maximally evade the immune system. Taken together, this dissertation provides several statistical tools that can be applied to better understand the fundamental dynamics underlying tumor-immune co-evolution and immunotherapy.