Mean curvature flow deforms a submanifold in the direction of its mean curvature vector. When the initial submanifold is Lagrangian in a Kahler-Einstein manifold, the solution will also be Lagrangian whenever it is smooth. It thus becomes a nice way to construct special Lagrangians. However, finite-time singularities may occur in general and cause the main difficulties. I will report some of my works on special solutions to Lagrangian mean curvature flow that is closely related to the study of singularities. A big part of the talk will concentrate on examples related to Schoen-Wolfson cones, which are the obstructions to the existence of special Lagranians in two-dimension.