Abstract: Phase retrieval is of paramount importance in a broad range of applications in engineering and imaging sciences. Mathematically, it amounts to solving a system of nonlinear quadratic equations, which is generally NP-hard. In this talk, we will give a numerical review of the problem and emphasize the different interests between the applied mathematicians and physicians. In other words, much research achievement of applied mathematicians has not intrigue the interests of physicians. One such reason is the simpler landscape of the resulting formulation. For example, the ambiguity solutions for practical phase retrieval is more complicated than phase retrieval from random sensing measurements. Thus the sound good solvers for random phase retrieval fails in locating a satisfying solution for practical phase retrieval. After we review the numerical algorithms for phase retrieval in literature, we introduce our recent work on phase retrieval, which tries its best to close the gap of random and practical phase retrieval. Our work gives some implications for designing the numerical algorithm for practical phase retrieval.