Cryptococcus neoformans var. grubii is the causative agent of cryptococcal meningitis, a significant source of mortality in immunocompromised individuals, typically human immunodeficiency virus/AIDS patients from developing countries. Despite the worldwide emergence of this ubiquitous infection, little is known about the global molecular epidemiology of this fungal pathogen. Here we sequence the genomes of 188 diverse isolates and characterize the major subdivisions, their relative diversity, and the level of genetic exchange between them. While most isolates of C. neoformans var. grubii belong to one of three major lineages (VNI, VNII, and VNB), some haploid isolates show hybrid ancestry including some that appear to have recently interbred, based on the detection of large blocks of each ancestry across each chromosome. Many isolates display evidence of aneuploidy, which was detected for all chromosomes. In diploid isolates of C. neoformans var. grubii (serotype AA) and of hybrids with C. neoformans var. neoformans (serotype AD) such aneuploidies have resulted in loss of heterozygosity, where a chromosomal region is represented by the genotype of only one parental isolate. Phylogenetic and population genomic analyses of isolates from Brazil reveal that the previously “African” VNB lineage occurs naturally in the South American environment. This suggests migration of the VNB lineage between Africa and South America prior to its diversification, supported by finding ancestral recombination events between isolates from different lineages and regions. The results provide evidence of substantial population structure, with all lineages showing multi-continental distributions; demonstrating the highly dispersive nature of this pathogen.