The field of population genetics has provided us with powerful methods for identifying genomic signals of natural selection from DNA sequence diversity and divergence data. However, current methods are not necessarily designed to identify signals of selection for genome structural change, or signals of selection for sex differences, though both scenarios appear to be evolutionarily important. I will present results from two unpublished projects that attempt to make some progress in addressing these issues. The first project focuses on a potential signal of selection associated with the evolution of chromosomal inversions. The second project focuses on signals of sex differences in selection. For each project, I will outline theoretical predictions for what we might expect to observe under different scenarios of selection for inversions or sex differences. I will then contrast these theoretical predictions with published data and new analyses of the UK Biobank.