Basidiomycota is one of two large phyla that , together with the Ascomycota , comprise the subkingdom Dikarya ( often referred to as the `` Higher Fungi '' ) within the Kingdom Fungi , that includes jelly and shelf , or bracket , mushrooms , puffballs , and stinkhorns ; and the rusts and smuts . Basidiomycota is one of two large phyla that , together with the Ascomycota , comprise the subkingdom Dikarya ( often referred to as the `` higher fungi '' ) within the Kingdom Fungi . More specifically the Basidiomycota include mushrooms , puffballs , stinkhorns , bracket fungi , other polypores , jelly fungi , boletes , chanterelles , earth stars , smuts , bunts , rusts , mirror yeasts , and the human pathogenic yeast Cryptococcus .