A fundamental goal of population genetics is to determine and quantify the interplay of mutation, natural selection, genetic drift and migration in shaping allelic frequency changes that underpin evolution-ary change. In this dissertation, I present computational, empirical and experimental approaches to address this goal. In the first chapter, I develop an approximate Bayesian computation (ABC) approach that co-estimates the selection strength and age of fixed beneficial mutations in single populations, by integrating a range of existing diversity, site frequency spectrum, haplotype and linkage disequilibrium based summary statistics. This approach is then extended to models of selection on standing variation in order to co-infer the frequency at which positive selection began to act upon the mutation. In the second chapter, I apply this method to an empirical study of convergent adaptation of blanched dorsal phenotypes in two lizard species to the newly formed White Sands system of New Mexico. Estimates of the age of the beneficial mutations underpinning the evolution of cryptic coloration are younger than the related geological shift and support a model of adaptation from de novo mutation. In the third chapter, I analyze the experimental evolution of H1N1 influenza virus populations under a combined protocol of two drugs with different modes of action: oseltamivir and favipiravir. Results indicate a complex interplay of mutation, selection and genetic drift, where selective sweeps around oseltamivir resistance mutations hitchhike deleterious mutations owing to the mutagenic effect of favipiravir to fixation. This effect reduces viral fitness and ac-celerates extinction via Muller’s ratchet, but at the risk of spreading both established and newly emerging oseltamivir resistance mutations.