A combination of selective and neutral evolutionary forces shape patterns of genetic diversity in nature. Among the insects, most previous analyses of the roles of drift and selection in shaping variation across the genome have focused on the genus Drosophila. A more complete understanding of these forces will come from analysing other taxa that differ in population demography and other aspects of biology. We have analysed diversity and signatures of selection in the neotropical Heliconius butterflies using resequenced genomes from 58 wild-caught individuals of H. melpomene, and another 21 resequenced genomes representing 11 related species. By comparing intra-specific diversity and inter-specific divergence, we estimate that 31% of amino acid substitutions between Heliconius species are adaptive. Diversity at putatively neutral sites is negatively correlated with gene density and positively correlated with recombination rate, indicating widespread linked selection. This process also manifests in significantly reduced diversity on longer chromosomes, consistent with lower recombination rates. Genetic hitchhiking around beneficial non-synonymous mutations has also had a significant impact on genetic variation in this species, but evidence for strong selective sweeps was limited overall. We did however identify two regions where distinct haplotypes have swept in different populations, leading to increased population differentiation. On the whole, our study suggests that positive selection is less pervasive in these butterflies as compared to fruit flies; a fact that curiously results in very similar levels of neutral diversity in these very different insects.