What are Basidiomycetes?
Basidiomycota and Ascomycota are often referred to as “higher fungi” (Subkingdom Dikarya within the Kingdom Fungi). Like Ascomycota, from which they are believed to have diverged, Basidiomycetes form long filamentous cells (hyphae). Unlike Ascomycota, which form sexual spores in a sac-like structure (Ascus), they reproduce sexually by forming pillar-like cells carrying four meiospores. This anatomy is name-giving (lat. Basidium = pillar). Basic information on classification and life-cycle can be found at the "tree of life" project.
The Basidiomycota further divides into the subphyla Pucciniomycotina, Ustilaginomycotina and Agaricomycotina (Hibbett et al. 2007, Myc. Research 111:509-547).
For phylogenetic relationships of the Basidiomycota see also
Ebersberger et al. 2012: Mol. Biol. Evol. 29: 1319-1334.