After Ricci flow, the mean curvature flow of submanifolds in a Riemannian manifold is the most natural and famous geometric flow, describing the gradient descent for the volume functional. It is also of interest to symplectic geometers, since in an ambient Kahler-Einstein manifold, the flow preserves the class of Lagrangian submanifolds. It is therefore of interest to understand the behaviour of the flow, in particular the nature of singularities. In this talk I hope to show the difference between the behaviour of singularities in the general case and the Lagrangian case, and give an exposition of my results regarding equivariant submanifolds.