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Digital holographic microscopy (DHM) is a topographic measurement technique that permits full-field, nondestructive, dynamic, quantitative amplitude, and phase-contrast imaging. The technique may realize the lateral resolution with submicron scale and the longitudinal resolution with subnanometer scale, respectively. Improving imaging quality has always been the research focus in DHM since it has a direct effect on the precise topographic measurement. In this paper, the recent progress on phase aberration compensation and coherent noise suppression is reviewed. Included in this review are the hologram spectrum’s centering judgment methods of side band in tilt phase error compensation, the physical and numerical compensation methods in phase aberration compensation, and the single-shot digital process methods in coherent noise suppression. The summaries and analyses for these approaches can contribute to improving the imaging quality and reducing the measurement error of DHM, which will further promote the wider applications of DHM in the topographic measurement fields, such as biology and micro-electro mechanical systems.