Extensive DNA data emerging from genome-sequencing projects have revitalized interest in the mechanisms of molecular evolution. Although the contribution of natural selection at the molecular level has been debated for over 30 years, the relevant data and appropriate statistical methods to address this issue have only begun to emerge. This paper will first present the predominant models of neutral, nearly neutral, and adaptive molecular evolution. Then, a method to identify the role of natural selection in molecular evolution by comparing within- and between-species DNA sequence variation will be presented. Computer simulations show that such methods are powerful for detecting even very weak selection. Examination of DNA variation data within and between Drosophila species suggests that 'silent' sites evolve under a balance between weak selection and genetic drift. Simulated data also show that sequence comparisons are a powerful method to detect adaptive protein evolution, even when selection is weak or affects a small fraction of nucleotide sites. In the Drosophila data examined, positive selection appears to be a predominant force in protein evolution.