In this dissertation we describe the microscopic behavior and emergent phenomena of evolutionary dynamics. We introduce frameworks that explicitly incorporate the effects of beneficial and deleterious mutations, and distributions of mutations. We treat a full distribution of mutations in adapting populations, providing a unified description of interference between established mutations. We compute experimentally observable parameters, including the speed of adaptation and the distribution of fixed mutations, for a general underlying distribution of available beneficial mutations. We identify an equivalence between the adaptive dynamics using a distribution of mutations, and the well known dynamics of mutations with a single fitness effect. Treating beneficial and deleterious mutations simultaneously, a dynamic mutation-selection balance emerges, which we argue is an evolutionarily stable state. The dynamic balance state describes a population in which rare beneficial mutations are sufficient to halt the stochastically driven extinction of subclasses in the population. This introduces a stationary state which we argue lies in an attractive basin, such that any generic adaptive population or fitness degrading population will approach the same equilibrium. The existence of this evolutionary "attractor" and its stability introduce this description as a new null expectation for any evolving population. We suggest that more complicated biological effects, such as changes in mutation rate, may be viewed as effective perturbations away from this state.