Research over the past two decades shows that both recombination and clonality are likely to contribute to the reproduction of all fungi. This view of fungi is different from the historical and still commonly held view that a large fraction of fungi are exclusively clonal and that some fungi have been exclusively clonal for hundreds of millions of years. Here, we first will consider how these two historical views have changed. Then we will examine the impact on fungal research of the concept of restrained recombination [Tibayrenc M, Ayala FJ (2012) Proc Natl Acad Sci USA 109 (48):E3305–E3313]. Using animal and human pathogenic fungi, we examine extrinsic restraints on recombination associated with bottlenecks in genetic variation caused by geographic dispersal and extrinsic restraints caused by shifts in reproductive mode associated with either disease transmission or hybridization. Using species of the model yeast Saccharomyces and the model filamentous fungus Neurospora, we examine intrinsic restraints on recombination associated with mating systems that range from strictly clonal at one extreme to fully outbreeding at the other and those that lie between, including selfing and inbreeding. We also consider the effect of nomenclature on perception of reproductive mode and a means of comparing the relative impact of clonality and recombination on fungal populations. Last, we consider a recent hypothesis suggesting that fungi thought to have the most severe intrinsic constraints on recombination actually may have the fewest.