i will present a joint work with martin li. minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. in this talk, i will describe a general existence theory for minimal surfaces with free boundary. in particular, i will show the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth euclidean domain. the minimal surfaces with free boundary were constructed using the min-max method. i will explain the basic ideas behind the min-max theory as well as our new contributions.