An interesting question in low-dimensional topology is, for a given 3-manifold, which 4-manifolds can be bounded by the 3-manifold. Answers to the question are particularly interesting since they demonstrate the big difference between topological and smooth categories in dimension four. In this talk, we survey some obstructions for the intersection forms of 4-manifolds to have the given 3-manifold as boundary. We apply these to completely classify definite intersection forms of 4-manifolds bounded by some families of lens space.