Within a fungal species, a subset of individuals may have more than the minimal complement of chromosomes. If the extra chromosomes are composed primarily of DNA not found in all representatives of the species, they are most appropriately referred to as supernumerary chromosomes. The patterns of repeated DNA sequences on certain supernumerary chromosomes suggest that they have a different evolutionary history from the essential chromosomes in the same genome. Supernumerary chromosomes can carry functional genes and, in at least two fungal species, genes on such chromosomes play important roles in host-pathogen interactions. Supernumerary chromosomes that confer an adaptive advantage in certain habitats, such as the ability to cause disease on a specific host, may be referred to as "conditionally dispensable" chromosomes in order to reflect their importance in some, but not all, growth conditions. In addition to describing the structural and functional characteristics of known supernumerary chromosomes in fungi, this review discusses the relative merits of the terms that have been used to describe them, and establishes experimental criteria for their identification.