In this review we will consider the retrieval of the wave at the exit surface of an object illuminated by a coherent probe from one or more measured diffraction patterns. These patterns may be taken in the near-field (often referred to as images) or in the far field (the Fraunhofer diffraction pattern, where the wave is the Fourier transform of that at the exit surface). The retrieval of the exit surface wave from such data is an inverse scattering problem. This inverse problem has historically been solved using nonlinear iterative methods, which suffer from convergence and uniqueness issues. Here we review deterministic approaches to obtaining the exit surface wave which ameliorate those problems.