The advent of next-generation sequencing has accelerated the search for somatic mutations that drive the initiation and progression of human cancers. Much emphasis has been placed on the few mutations that occur at high frequency either within or across cancer types. Yet most mutations in cancer genomes occur infrequently. Nevertheless, in aggregate, these rare mutations play a defining role in as many as one-fourth of all human cancers. Distinguishing which rare mutations, amidst a sea of incidental passenger mutations, drive critical molecular, biological, and clinical phenotypes is a foremost challenge of precision oncology. Here, this dissertation discusses complementary computational approaches to identify putative driver mutations in cancer with a focus on how such mutations can reveal novel biological and clinical insights. The two computational approaches leverage 1) recurrence, one of the best markers of selection, to identify mutations that arise more frequently than expected by chance and 2) protein structures, as orthogonal biological evidence, to credential even private driver mutations through significantly recurrent mutational clusters. These methods are applied to mutational data obtained from both retrospectively sequenced human tumor samples and prospectively sequenced cancer patients who received medical care at Memorial Sloan Kettering. As clinical actionability necessitates first understanding the prevalence and properties of driver mutations across diverse cancer types, exploration of patterns of driver mutation emergence as well as validating novel mutations reveal new insights into the pathogenesis and therapeutic sensitivity of human cancers.