  We define the notion of a moment map and reduction in both generalized
complex geometry and generalized K\"{a}hler geometry. As an application, we
give very simple explicit constructions of bi-Hermitian structures on $\C\P^n$,
Hirzebruch surfaces, the blow up of $\CP^2$ at arbitrarily many points, and
other toric varieties, as well as complex Grassmannians.
