  We introduce the notion of twisted generalized complex submanifolds and
describe an equivalent characterization in terms of Poisson-Dirac submanifolds.
Our characterization recovers a result of Vaisman. An equivalent
characterization is also given in terms of spinors. As a consequence, we show
that the fixed locus of an involution preserving a twisted generalized complex
structure is a twisted generalized complex submanifold. We also prove that a
twisted generalized complex manifold has a natural Poisson structure. We also
discuss generalized Kaehler submanifolds.
