Chromosomal inversions have been an enduring interest of population geneticists since their discovery in Drosophila melanogaster. Numerous lines of evidence suggest powerful selective pressures govern the distributions of polymorphic inversions, and these observations have spurred the development of many explanatory models. However, due to a paucity of nucleotide data, little progress has been made towards investigating selective hypotheses or towards inferring the genealogical histories of inversions, which can inform models of inversion evolution and suggest selective mechanisms. Here, we utilize population genomic data to address persisting gaps in our knowledge of D. melanogaster's inversions. We develop a method, termed Reference-Assisted Reassembly, to assemble unbiased, highly accurate sequences near inversion breakpoints, which we use to estimate the age and the geographic origins of polymorphic inversions. We find that inversions are young, and most are African in origin, which is consistent with the demography of the species. The data suggest that inversions interact with polymorphism not only in breakpoint regions but also chromosome-wide. Inversions remain differentiated at low levels from standard haplotypes even in regions that are distant from breakpoints. Although genetic exchange appears fairly extensive, we identify numerous regions that are qualitatively consistent with selective hypotheses. Finally, we show that In(1)Be, which we estimate to be ∼60 years old (95% CI 5.9 to 372.8 years), has likely achieved high frequency via sex-ratio segregation distortion in males. With deeper sampling, it will be possible to build on our inferences of inversion histories to rigorously test selective models-particularly those that postulate that inversions achieve a selective advantage through the maintenance of co-adapted allele complexes.