In this talk, we consider the Cauchy problem of nonlinear dispersive equation. Nonlinear dispersive equations include an important class of equations such as the nonlinear Schrodinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. There are many important issues as wellposedness, blowup, scattering, stability and so on. In this time, we shall focus on wellposedness of fractional Schrodinger equation. Wellposedness of initial value problem depends on regularity of initial datum. I will present some results and methods regarding high regularity wellposedness, low regularity wellposedness and probabilistic wellposedness.