Understanding the genetics underlying the speciation process has been a long-standing goal of evolutionary biology. Studying inter-population crosses can elucidate the genetic architecture of reproductive isolation and, ultimately, the process of speciation. Hybridization between two species is often maladaptive and results in offspring with decreased fitness compared to the parental forms. Recently, with the development of molecular and genomic tools, it has become possible to understand how and when reproductive isolation arises and what are the underlying mechanisms in the evolution of genetic incompatibilities. Heliconius is a genus of neotropical butterfly best know for their Müllerian mimicry. Here I focus on Heliconius cydno and Heliconius melpomene, two hybridising sympatric species with low levels of inter-specific hybridisation that nonetheless results in genome-wide signatures of admixture. I show that hybrids develop ovarian tissue and, occasionally, oocytes; and use genomic approaches to examine several potential mechanisms underlying post-zygotic isolation between H. cydno and H. melpomene. Firstly, I investigate evolution by gene duplication and identify loci putatively under divergent selection that may play a role in species divergence and speciation. Secondly, I quantify sexually dimorphic expression in H. melpomene, and calculate rates of molecular evolution between H. melpomene and H. erato. Thirdly, I identify differentially expressed genes in the H. cydno x H. melpomene F1 hybrids that may be involved in the species barrier. Finally, investigate whether epigenetic silencing mechanisms could underlie post-zygotic isolation between H. cydno and H. melpomene by quantifying transposable element expression and small RNAs. Overall, I identify loci that merit further investigation for their potential in maintaining reproductive barriers between these two species. I show that different regions of the genome evolve at different molecular rates but there is no faster-Z effect, and consider how might this affect evolution of reproductive isolation. Finally, I show that aberrant epigenetic silencing, a mechanism behind hybrid sterility that is common in other species, is not correlated with post-zygotic isolation between H. cydno and H. melpomene.