Under the condition of the framework of discrete fractional Fourier transform (DFRFT),the research on the phase retrieval problem of complex signals and images is reviewed. Firstly,based on the basic Gerchberg-Saxton (G-S) algorithm and the diversity of the DFRFT orders,a great number of numerical simulations are performed for the case of complex image and three DFRFT orders. The results indicate that when the difference of these orders is large,the two algorithms are quite efficient,and the whole performance of the serial version is better than the parallel one. Secondly,for the case of 1-D complex signal,an algorithm based on the non-linear least-squares is studied. This algorithm converts the original problem into the optimization of a non-linear least-squares,and then is solved by the Levenberg-Marquardt algorithm of Moré′s form. With two DFRFT amplitudes of arbitrary orders,the algorithm can reconstruct quite accurate phase distribution,and its performance for noisy amplitudes is also satisfying.