This chapter discusses several methods of establishing the local and global wellposedness of nonlinear dispersive PDEs. These include the classical energy method, the oscillatory integral method, the restricted norm method, and the normal form transform. The energy method relies on parabolic regularization and a priori energy bounds. The oscillatory integral method and the restriced norm methods rely on the smoothing properties of the linear propagator quantified by space-time linear and multilinear estimates. We also introduce methods that are useful in proving the illposedness of nonlinear dispersive PDEs in the presence of rough initial data.