Imaging of microscopic objects is of fundamental importance, especially in life sciences. Recent fast progress in electronic detection and control, numerical computation, and digital image processing, has been crucial in advancing modern microscopy. Digital holography is a new field in three-dimensional imaging. Digital reconstruction of a hologram offers the remarkable capability to refocus at different depths inside a transparent or semi-transparent object. Thus, this technique is very suitable for biological cell studies in vivo and could have many biomedical and biological applications. A comprehensive review of the research carried out in the area of digital holographic microscopy (DHM) for live-cell imaging is presented. The novel microscopic technique is non-destructive and label-free and offers unmatched imaging capabilities for biological and bio-medical applications. It is also suitable for imaging and modelling of key metabolic processes in living cells, microbial communities or multicellular plant tissues. Live-cell imaging by DHM allows investigation of the dynamic processes underlying the function and morphology of cells. Future applications of DHM can include real-time cell monitoring in response to clinically relevant compounds. The effect of drugs on migration, proliferation, and apoptosis of abnormal cells is an emerging field of this novel microscopic technique.