Genomic regions determining sexual compatibility often display recombination suppression, as occurs in sex chromosomes, plant self-incompatibility loci and fungal mating-type loci. Regions lacking recombination can extend beyond the genes determining sexes or mating types, by several successive steps of recombination suppression. Here we review the evidence for recombination suppression around mating-type loci in fungi, sometimes encompassing vast regions of the mating-type chromosomes. The suppression of recombination at mating-type loci in fungi has long been recognized and maintains the multi-allelic combinations required for correct compatibility determination. We review more recent evidence for expansions of recombination suppression beyond mating-type genes in fungi ("evolutionary strata"), which have been little studied and may be more pervasive than commonly thought. We discuss testable hypotheses for the ultimate (evolutionary) and proximate (mechanistic) causes for such expansions of recombination suppression, including i) antagonistic selection, ii) association of additional functions to mating-type, such as uniparental mitochondria inheritance, iii) accumulation in the margin of non-recombining regions of various factors, including deleterious mutations or transposable elements due to relaxed selection, or neutral rearrangements due to genetic drift. The study of recombination suppression in fungi could thus contribute to our understanding of recombination suppression expansion across a broader range of organisms.