For the last 50 years or longer, it has been a basic question in topology to study differential structures of a given manifold. In the early 80's, Donaldson used anti-self solutions of the Yang-Mills equation to study differentiable 4-manifolds and construct a very useful class of differentiable invariants for 4-manifolds. In particular, he was able to show that a topological 4-manifold may have different differentiable structures. In this talk, I will discuss geometric methods in studying 4-manifolds and in particular, some recent progress.