  We review the construction of regular p-brane solutions of M-theory and
string theory with less than maximal supersymmetry whose transverse spaces have
metrics with special holonomy, and where additional fluxes allow for brane
resolutions via transgression terms. We summarize properties of resolved
M2-branes and fractional D2-branes, whose transverse spaces are Ricci flat
eight-dimensional and seven-dimensional spaces of special holonomy. Recent
developments in the construction of new G_2 holonomy spaces are also reviewed.
