A solution of the Hamitonian stationary variational problem is a Lagrangian submanifold (of a symplectic manifold with compatible Riemannian metric) whose volume is stationary under Hamiltonian variations. In joint work with Adrian Butscher, we construct families of small Hamiltonian stationary Lagrangian tori near a point in a Kahler four-manifold, under a non-degeneracy condition on the complex curvature tensor at the point.