Abstract: Hamiltonian stationary Lagrangian (HSL) submanifolds are critical points of the volume functional under Hamiltonian variations. They include special Lagrangians (i.e. Lagrangian submanifolds with zero mean curvature), for example, lines and circles are Hamiltonian stationary in the plane. We will discuss compactness of immersed compact HST submanifolds in $C^n$ with volume and (extrinsic) total curvature bounds and a removable singularity result. This is joint work with Micah Warren.