We will discuss recent joint works with J. Marzuola and D. Tataru that focus on local existence for generic quasilinear Schrodinger equations with data in low regularity spaces. The Mizohata integrability conditions plays an essential role in choosing appropriate spaces, and in order to incorporate the necessary decay, we choose Sobolev spaces that are adapted to include a summability over a partition of space into cubes. The primary estimate is a local smoothing estimate, which is adapted to these spaces.