Two Groups - classifying fungi into ascomycetes and basidiomycetes:
Corticioid, stereoid and coral fungi
basidia lining the undersides of the fruiting bodies
The corticioid and stereoid fungi have basidia lining the undersides of the fruiting bodies. The corticioid fungi have sheet-like fruiting bodies - often smooth but also found with minor bumps, ridges, spines, etc on the otherwise two-dimensional sheets. The stereoid fruiting bodies also have generally smooth undersides but are bracket-like or with a stem - and therefore differ from the corticioid fungi by being markedly three-dimensional. The following diagram, represents a corticoid fruiting body (the brighter brown) growing on the underside of a piece of wood lying on the ground. You can see the basidia protruding into the air.
Clavaria zollingeri (right)
A funnel-shaped stereoid fungus such as Cymatoderma elegans var. lamellatum has the basidia on the underside of the sloping funnel area.
In a coral fungus, such as Clavaria zollingeri the basidia are found on many of the branches, as shown in this diagram.