In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criterion, we dualize the results to submersions and we make a few comments on generalized complex mappings. Then, we discuss submanifolds of generalized Kahler manifolds that have an induced generalized Kahler structure. These turn out to be the common invariant submanifolds of the two classical complex structures of the generalized Kahler manifold.