I shall discuss recent results on mean curvature flow in higher codimension. The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. This should be considered as the gradient flow of area functional on the space of submanifolds. The analytic nature is a nonlinear parabolic system of partial differential equations. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity, global existence and convergence of the flow in various ambient spaces and arbitrary codimensions were proved. I shall explain the techniques involved as well as the results obtained. The applications in differential topology and mirror symmetry will also be discussed.