Natural selection is a cornerstone of modern biology and remains the primary explanation for how species adapt to their environment. Population genetic methods have been developed to quantify natural selection in the genome. However, the factors and mechanisms leading to variation in type and strengths of selection across the genome are still unclear. In this talk, I am going to present a novel population genetic approach for estimating genetic dominance.  Applying this novel approach to data from Arabidopsis,I find that mutations are predominantly recessive. Specifically, mutations in weakly expressed genes are more recessive than mutations in strongly expressed genes. This suggests that, contrary to classical models of the evolution of dominance, differences in dominance between genes are a consequence of the cost of gene expression.In the second half of my talk, I discuss population genetic signatures of positive selection. I present a new approach for quantifying positive selection that is robust to demography and ascertainment bias. Applying this method to 1165 ancient western Eurasian genomes identified multiple genes and pathways that have experienced strong positive selection after modern humans moved out of Africa around 50-55ka. Importantly, our analysis of ancient DNA reveals signatures of past selection that are obscured in modern populations as a result of genetic mixing during the Bronze Age.