Mosquitoes of the Anopheles gambiae species complex are the primary vector for malaria in sub-Saharan Africa, causing over 600,000 deaths annually due to the disease. However, there is still much uncertainty regarding their demography, despite its importance for strategies to reduce transmission. In this work I use population genomic data and simulations to investigate the demography of these species. I focus on analyses involving rare variants in the genome, specifically doubletons, to enable fine scale demographic inference. I first examine doubleton mutations in the Anopheles gambiae genome, using data from the Anopheles gambiae 1000 Genomes project. I estimate that up to 16% of these are recurrent mutations, and develop a probabilistic approach to identifying those most likely to be non-recurrent. Applying this I observe that shared ancestral DNA (haplotypes) around these doubletons convey information on several biological processes including, crucially, demography. I then examine the effects that different aspects of demography have on doubleton haplotypes, by developing a coalescent genomic simulation framework utilising a 2-D stepping stone model. I show both population size, N, and the number of migrants, Nm, have clear, independent impacts on haplotypes, and that these discrete models can be used to approximate continuous space. Finally, I extend this simulation framework to approximate the habitat and sampling of An. gambiae in West Africa to attempt demographic parameter inference using approximate Bayesian computation. I show that doubleton haplotypes in this region potentially reveal patterns of relatedness missed by common variants, and that with these simulations both population density and dispersal rates can be inferred, although the estimates obtained differ from previous estimates in the literature. Overall, my work demonstrates that rare variant haplotypes are informative on the demography of An. gambiae and warrants further development of this parameter inference approach.