  We systematically revisit the description of $D$-branes on orbifolds and the
classification of their charges via K-theory. We include enough details to make
the results accessible to both physicists and mathematicians interested in
these topics. The minimally charged branes predicted by K-theory in Z_N
orbifolds with $N$ odd are only BPS. We confirm this result using the boundary
state formalism for Z_3. For Z_N x Z_N orbifolds with and without discrete
torsion, we show that the K-theory classification of charges agrees with the
boundary state approach, largely developed by Gaberdiel and collaborators,
including the types of representation on the Chan-Paton factors.
