I will speak on a recent joint study with J. Marzuola and D. Tataru which proves low regularity local well-posedness for quasilinear Schroedinger equations. Similar results were previously proved by Kenig, Ponce, and Vega in much higher regularity spaces using an artificial viscosity method. Our techniques, and in particular the spaces in which we work, are motivated by those used by Bejenaru and Tataru for semilinear equations.