The genetic variation among extant life forms reflects the outcomes of evolution. The fodder of evolution – germline mutations – is shaped by the interplay among evolutionary forces – notably natural selection and random genetic drift. In turn, these forces leave footprints recorded in the genetic variation of extant life forms. Characterizing these footprints to understand how evolution works is at the heart of population genetics. To this end, massive datasets of genetic variation have opened new avenues of research, around how mutation rates evolve for instance, and reinvigorated long standing questions in population genetics, notably about the genetic basis of adaptation. In turn, theoretical models of evolution inform what kind of footprints we expect evolution to leave behind in such data. Two theoretical models that investigate open questions in population genetics are described in this thesis. In Chapter 1, I consider the evolution of germline mutation rates, particularly on short evolutionary timescales, and ask if recently observed variation in mutation rates among human lineages could be explained by evolution at genetic modifiers of mutation rates. Genetic modifiers of mutation rates are expected to evolve under purifying selection: mutations at modifiers that increase mutation rates (“mutator alleles”) should be selected against, because they increase the burden of deleterious mutations in individuals who carry them. The frequencies of mutator alleles are also affected by mutation, genetic drift, and demographic processes. We model the evolution of mutator alleles under the interplay of these forces and characterize the dynamics at mutation rate modifiers as a function of the efficacy of selection acting on them. We find that modifiers under intermediate selection have the greatest contribution to variation in mutation rates between distantly related populations, but only variation at strongly selected modifiers turns over fast enough to explain variation in mutation rates among human lineages. We also predict that strongly selected modifiers could be potentially identified in the contemporary datasets of human pedigrees used to study germline mutations. In Chapter 2, I consider a central and enduring question in evolutionary biology: whether adaptation typically arises from few large effect changes or from many small effect changes. Both sides are supported by ample evidence. Yet it is unclear how to translate this evidence into general answers about the genetic basis of adaptation, in part because different methodologies have different limitations and ask different questions. Theory may offer a way out of this quagmire or at least a start. To this end, we reframe the question in terms of traits and ask: how does the genetic basis of adaptation depend on the ecological and genetic attributes of a trait? To start answering this question, I model adaptation in a simple yet highly relevant setting. I consider a trait under stabilizing selection and assume the distribution of trait values in the population is initially at mutation-selection-drift-balance. I then characterize the adaptive response that is elicited by a sudden change in the environment. I find that the adaptive response, and notably the probability that adaptation arises from the fixation of large effect alleles, depends on the size of the environmental change and the genetic architecture of the trait. These attributes are measurable and can be directly related to the disparate evidence that we have about the genetic basis of adaptation. Thus, this kind of modeling may help translate such evidence into general conclusions about how traits evolve. My thesis work was interrupted by the global COVID-19 pandemic, and in response to this pandemic, governments around the world implemented shelter-in-place protocols. However, essential workers were exempt from these protocols, potentially decreasing their efficacy. In Chapter 3, we describe our epidemiological project, aimed at understanding the impact of essential workers on epidemic control. To this end, we model three different archetypes of essential workers under a reasonably realistic SEIR model of the COVID-19 pandemic. We find that the different social interactions that essential workers maintain qualitatively changes their personal risk of infection and the spread of the overall epidemic. These results highlight the utility of not considering essential workers as a monolithic group but instead distinguishing between the impact of different types of essential workers on epidemic control.