In this talk, we introduce the main features of the Lagrangian mean curvature flow. We will first discuss some differences between mean curvature flow in higher codimension and the more familiar mean curvature flow of hypersurfaces. After introducing some salient facts about Lagrangian submanifolds, we show that Lagrangian immersions in a Calabi-Yau manifold are a preserved class under the mean curvature flow, and discuss the evolution equations of certain geometric quantities. In the remaining time, we will touch upon the theory of singularity formulation and give a few concrete examples of the flow.