The immune system plays a dual role during neoplastic progression. It can suppress tumor growth by eliminating cancer cells, and also promote neoplastic expansion by either selecting for tumor cells that are fitter to survive in an immunocompetent host or by establishing the right conditions within the tumor microenvironment. First, I present a model to study the dynamics of subclonal evolution of cancer. I model selection through time as an epistatic process. That is, the fitness change in a given cell is not simply additive, but depends on previous mutations. Simulation studies indicate that tumors are composed of myriads of small subclones at the time of diagnosis. Because some of these rare subclones harbor pre-existing treatment-resistant mutations, they present a major challenge to precision medicine. Second, I study the question of self and non-self discrimination by the immune system, which is fundamental in the field in cancer immunology. By performing a quantitative analysis of the biochemical properties of thousands of MHC class I peptides, I find that hydrophobicity of T cell receptors contact residues is a hallmark of immunogenic epitopes. Based on these findings, I further develop a computational model to predict immunogenic epitopes which facilitate the development of T cell vaccines against pathogen and tumor antigens. Lastly, I study the effect of early detection in the context of Ebola. I develope a simple mathematical model calibrated to the transmission dynamics of Ebola virus in West Africa. My findings suggest that a strategy that focuses on early diagnosis of high-risk individuals, caregivers, and health-care workers at the pre-symptomatic stage, when combined with public health measures to improve the speed and efficacy of isolation of infectious individuals, can lead to rapid reductions in Ebola transmission.