It has become quite easy to sequence genomes. But as the amount of available sequence data expands exponentially, it remains hard to understand what this data means. The only complete framework for interpreting the genetic diversity we observe assumes that all mutations are selectively neutral. But it is becoming increasingly clear that natural selection is pervasive in nature, and has far-reaching impacts on patterns of diversity. It is essential to understand these impacts if we are to learn from sequence data about how populations adapt and respond to various challenges. Unfortunately, standard population genetic techniques are of limited use in understanding this selected diversity. This is particularly true in asexual populations or on short distance scales in sexual genomes, because mutations are physically linked to each other, and hence the dynamics of different mutations are not independent. I will present a new framework for analyzing the evolutionary dynamics of selection in asexual populations, which involves a self-consistent approach to the coupled behavior of many fluctuating mutant lineages. I will describe preliminary work on how selection changes the character of the genetic diversity these populations maintain. This provides a potential basis for techniques to learn from the genetic diversity in natural asexual populations, including a wide variety of microbes and viruses, as well as on short distance scales in sexual genomes.