The theory of hyperbolic systems is heavily based on studying their stable and unstable foliations. The main difficulty in studying partially hyperbolic systems is the fact that their central foliations may fail to be (uniquely) integrable. Consider a continuous vector field. It is always integrable (there is an integral curve through every point). Of course, it can fail to be uniquely integrable. Higher dimensional distributions (even if they are smooth) are generically non-integrable. On the other hand, in some situations it is known (for instance, from dynamical considerations) that a distribution that is only continuous is nonetheless integrable. However, it may fail to be uniquely integrable. Furthermore, it is not clear that it admits approximations by tangent distributions of (C^0) foliations (with C^1 leaves). We will show that such approximations exist for 2-D distributions in a 3-manifold if the distribution is formed by two vector fields if one of the fields is uniquely integrable. This is the case for central-stable foliations of 3-D partially hyperbolic systems. This result is a key ingredient in proving that, for instance, S^3 admits no partially hyperbolic diffeomorphisms. The proof is a combination of the approximation described above, a compactness argument, and a version of Novikov's Compact Leaf Theorem. More generally, for a partially hyperbolic diffeomorphism of a 3-manifold with an abelian fundamental group, its action on the first homologies is also partially hyperbolic (it has eigenvalues \alpha>1 and \beta<1). The talk is based on a joint work with M. Brin and S. Ivanov.