  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 brane
resolutions via transgression terms. We focus on the properties of resolved
M2-branes and fractional D2-branes, whose transverse spaces are Ricci flat
eight-dimensional and seven-dimensional spaces of special holonomy. We also
review fractional M2-branes with transverse spaces corresponding to the new
two-parameter Spin(7) holonomy metrics, and their connection to fractional
D2-branes with transverse spaces of G_2 holonomy.
