According to the University of California Museum of Paleontology, fungi have four major classifications: chytrids, bread molds, yeasts and sacs and club fungi. Each classification differs mostly by method of sexual reproduction, since all fungi divisions utilize spore reproduction in a slightly different manner.
The formal names for these classifications are: chytridiomycota (chytrids), zygomycota (bread molds), ascomycota (yeasts) and basidiomycota (club fungi). Additionally, there are two polyphyletic groups that are not recognized by the scientific community. These are the deuteromycota (asexual fungi that do not reproduce sexually) and lichens (symbiotic communities of fungi and algae). Together, these groups are all of the formal and informal classifications for fungi.