Owing to its high resolution, sensitivity, imaged field of view, and frame rate acquisition, Digital Holographic Microscopy (DHM) stands out among the Quantitative phase imaging (QPI) techniques to reconstruct high-resolution phase images from micrometer-sized samples, providing information about the sample's topography and refractive index. Despite the successful performance of DHM systems, their applicability to in-situ clinical research has been partially hampered by the need for a standard phase reconstruction algorithm that provides quantitative phase distributions without any phase distortion. This invited talk overviews the current advances in computational DHM reconstruction approaches from semiheuristic to learning-based approaches.