Special Lagrangians are important examples of minimal submanifolds in Calabi-Yau manifolds introduced by Harvey-Lawson. In this talk, we will provide some new examples of special Lagrangian submanifolds in certain log Calabi-Yau manifolds via the techniques of Lagrangian mean curvature flow. We will also talk about the applications to mirror symmetry, including the existence of special Lagrangian fibration in some log Calabi-Yau surfaces. This is base on a joint work with T. Collins and A. Jacob.