  Twisted $K$-homology corresponds to $D$-branes in string theory. In this
paper we compare two different models of geometric twisted $K$-homology and get
their equivalence. Moreover, we give another description of geometric twisted
$K$-homology using bundle gerbes. We establish some properties of geometric
twisted $K$-homology. In the last part we construct $T$-duality isomorphism for
geometric twisted $K$-homology.
