Aspergillus fumigatus has long been considered to reproduce only by asexual means. However, accumulating evidence suggest that a sexual stage for A. fumigatus may yet be identified. We describe results from published and ongoing studies involving population genetic analyses, genome analysis, studies of mating-type gene presence and distribution, expression of sex-related genes, and taxonomic work which support the assertion that A. fumigatus has the potential to reproduce by sexual means. The consequences of sexual reproduction for the population biology and disease management of the species are discussed. The possible mechanisms of evolution of asexuality are then considered. It is proposed that asexual species may arise in one step by mutation or loss of a key gene(s), and/or there may be a 'slow decline' in sexual fertility within the species as a whole. Thus, it is argued that species should not be considered simply as sexual or asexual, but rather as individual isolates being present on a continuum of sexual fertility, with the implications for understanding sexuality/asexuality in A. fumigatus discussed.