In-line digital holography is widely applied in many areas due to its simple optical path, low requirement of coherence and fully utilization of camera′s bandwidth. The reconstruction quality of in-line digital holography, however, suffers from the superposition of twin-image contamination, which can be solved via phase retrieval algorithm. By iteratively applying certain constraints on an estimate of an object in real and reciprocal domain, the real image is well seperated from the unwanted components. The recording and reconstruction process of in-line digital holography and fundemental phase retrieval methods including Gerchberg-Saxton (GS), error reduction (ER) and hybrid input-output (HIO) algorithms are introduced. Then, the phase retrieval algorithms for in-line digital holography is divided into four categories, i.e., constraints, multiple axially recording, wavelength divergency and initial guess. The constraints and experimental results of these phase retrieval algorithms are listed. Finally, a prospect is given for the possible improvement and potential applications of phase retrieval methods in in-line digital holography.