Lagrangian mean curvature flow has received much attention in the past fifteen years. It is conjectured by Thomas and Yau that a stable Lagrangian isotopy class in a Calabi-Yau manifold contains a smooth special Lagrangian and the deformation process to find the special Lagrangian representative can be realized by the mean curvature flow. The key observation is that, in this setting, a submanifold which is initially Lagrangian will remain Lagrangian when evolving under mean curvature flow.