We discuss the convergence problem for formal holomorphic maps taking a real-analytic submanifold in some complex Euclidean space into a real-analytic set in some other complex space, i.e. the question whether every such formal map necessarily converges. Our main result shows that if there exists a divergent formal map, then the target set has to contain some complex variety. The technique used to prove this result also solves convergence problems for sources and targets foliated by complex manifolds, and can be adapted to treat other regularity questions for CR maps.
