The Drosophila nasuta species complex contains over a dozen recently diverged species that are distributed widely across South-East Asia, and which shows varying degrees of pre- and postzygotic isolation. Here, we assemble a high-quality genome for D. albomicans using single-molecule sequencing and chromatin conformation capture, and draft genomes for 11 additional species and 67 individuals across the clade, to infer the species phylogeny and patterns of genetic diversity in this group. Our assembly recovers entire chromosomes, and we date the origin of this radiation ∼2 Ma. Despite low levels of overall differentiation, most species or subspecies show clear clustering into their designated taxonomic groups using population genetics and phylogenetic methods. Local evolutionary history is heterogeneous across the genome, and differs between the autosomes and the X chromosome for species in the sulfurigaster subgroup, likely due to autosomal introgression. Our study establishes the nasuta species complex as a promising model system to further characterize the evolution of pre- and postzygotic isolation in this clade.