Proving that Galois representations in many situations arise from automorphic forms has been a major theme in number theory for at least two decades. However, most of the existing work concerns the situation when the mod p reduction of the Galois representation (i.e., the residual representation) is irreducible and when the number field is totally real. We will present new modularity results for n-dimensional residually reducible Galois representations over arbitrary number fields. This is joint work with T. Berger.