As national governments scale up mass drug administration (MDA) programs aimed to combat neglected tropical diseases (NTDs), novel selection pressures on these parasites increase. To understand how parasite populations are affected by MDA and how to maximize the success of control programmes, it is imperative for epidemiological, molecular and mathematical modelling approaches to be combined. Modelling of parasite population genetic and genomic structure, particularly of the NTDs, has been limited through the availability of only a few molecular markers to date. The landscape of infectious disease research is being dramatically reshaped by next-generation sequencing technologies and our understanding of how repeated selective pressures are shaping parasite populations is radically altering. Genomics can provide high-resolution data on parasite population structure, and identify how loci may contribute to key phenotypes such as virulence and/or drug resistance. We discuss the incorporation of genetic and genomic data, focussing on the recently sequenced Schistosoma spp., into novel mathematical transmission models to inform our understanding of the impact of MDA and other control methods. We summarize what is known to date, the models that exist and how population genetics has given us an understanding of the effects of MDA on the parasites. We consider how genetic and genomic data have the potential to shape future research, highlighting key areas where data are lacking, and how future molecular epidemiology knowledge can aid understanding of transmission dynamics and the effects of MDA, ultimately informing public health policy makers of the best interventions for NTDs.