It is known that many simply connected, smooth topological
4-manifolds admit infinitely many exotic smooth structures. The
smaller the Euler characteristic, the harder it is to construct
exotic smooth structure. In this talk, we construct exotic smooth
structures on small 4-manifolds such as CP^2#k(-CP^2) for k = 2, 3,
4, 5 and 3CP^2#l(-CP^2) for l = 4, 5, 6, 7. We will also discuss the
interesting applications to the geography of minimal symplectic
4-manifolds.