A complex manifold is said to be Stein if it can be represented as a closed complex submanifold of a complex Euclidean space. By a classical theorem of Grauert every continuous map from a Stein manifold to a complex homogeneous manifold is homotopic to a holomorphic map (the Oka-Grauert principle). In this talk we shall examine the validity of this principle and its limitations for more general target manifolds. We will see that the result holds completely universally if we also allow homotopic variations of the complex structure on the source manifold. If X is a Stein surface, another limitation is imposed by the adjunction inequalities for smoothly embedded oriented real surfaces, thereby connecting our problem with four dimensional topology.