In this thesis I have investigated variation in the effective population size (Ne) between species, and the impact that this population genetics parameter has on molecular evolution. In Chapter 1 I review literature in order to outline our present understanding of variation in Ne, both between species and within a genome. In Chapter 2 I determine whether island species have lower effective population sizes than their mainland counterparts. I found that island species did not differ substantially from mainland species in terms of molecular evolution, despite their considerably smaller ranges. Chapter 3 examines the role of life history and demographic traits in shaping molecular evolution in mammals. Using mitochondrial DNA, I found significant correlations with species range for both genetic diversity (pS) and the efficiency of selection (pN/pS). Both latitude and body mass are also predictive of pS. However, these relationships are surprisingly weak. Additionally, no trait was predictive of nuclear molecular evolution. In Chapter 4 I determine whether there is adaptive evolution in animal mitochondrial DNA using McDonald-Kreitman style tests. While mitochondrial evolution is dominated by deleterious mutations, mitochondria also experience adaptive evolution, such that 26% of all nonsynonymous mutations are fixed by adaptive evolution. I also found evidence to suggest that the rate of adaptive evolution is correlated to Ne. In Chapter 5 I explore the relationship between pN/pS and pS, two variables that are expected to depend on Ne. I quantified the relationship between pS and pN/pS, after controlling for the statistical nonindependence between the two, to show that as πS doubles, πN/πS is reduced by 34%. I also investigated whether the slope of the regression between these variables is predicted by the shape parameter of the distribution of fitness effects. In Chapter 6 I give a general overview of my research, and bring together the key findings of this thesis.