  We describe various approaches to Coleff-Herrera products of residue currents
$R^j$ (of Cauchy-Fantappi\`e-Leray type) associated to holomorphic mappings
$f_j$. More precisely, we study to which extent (exterior) products of natural
regularizations of the individual currents $R^j$ yield regularizations of the
corresponding Coleff-Herrera products. Our results hold globally on an
arbitrary pure-dimensional complex space.
