Mean curvature flow (MCF) is the negative gradient flow for the area functional in Euclidean spaces, or more generally in Riemannian manifolds. Over the past few decades, there have been substantial progress towards our knowledge on the analytic and geometric properties of MCF. For compact surfaces without boundary, we have a fairly good understanding of the convergence and singularity formation under the flow. In this talk, we will discuss some recent results on MCF of surfaces with boundary. In the presence of boundary, suitable boundary conditions have to be imposed to ensure the evolution equations are well-posed. Two such boundary conditions are the Dirichlet (fixed or prescribed) and Neumann (free or prescribed contact angle) boundary conditions. We will mention some new phenomena in contrast with the classical MCF without boundary. We give a convergence result for mean curvature flow of convex hypersurfaces with free boundary. This is joint work with Sven Hirsch. (These works are partially supported by RGC grants from the Hong Kong Government.).