The mean curvature flow is the heat equation of submanifolds. A submanifold evolves in order to decrease its area as fast as possible along this process whose the stationary phase correspond to minimal submanifolds. A distinguished class of minimal submanifolds of Calabi-Yau manifolds are called special Lagrangians. Several important conjectures on Calabi-Yau manifolds demand deep understanding of the structure of special Lagrangians. However, so far there is no general procedure of constructing special Lagrangians. We propose to deform a Lagrangian submanifold to a special one by the mean curvature flow. The flow may develop singularities along the process. In order to complete the flow, we shall investigate the formation and surgeries of singularities.