In 1948, GABOR D proposed the concept of holography, which provided a pioneering technical solution for the quantitative analysis of light-wave fields. After more than 70 years of development, computational imaging and quantitative phase imaging based on holography has become an important tool for the quantitative measurement of the light-wave field. It provides a new observation dimension for the fields of physics, biology and materials science, and builds a bridge of optical imaging and light scattering. It breaks through the physical limitations of conventional optical imaging systems. It plays a crucial role in the pathological study of diseases and the characterization of materials. From the point of signal analysis, the process of holographic recording and reconstruction can be regarded as the transformation between the complex domain and the real domain. The mathematical principle and physical realization of digital holography are discussed. In addition, the new challenges of holographic imaging are summarized in the prospects.The propagation of wavefront is described by the complex-amplitude distribution. The idea of digitally reconstructing the optical wavefront first appeared in the 1960 s. However, there was array-detector-based holographic imaging for applications until the 1990 s. At that time, two sectors of technology have been important developments. One of which is that microtechnological processes have resulted in CCD arrays with sufficiently small pixels to fulfill the Shannon condition, which is suitable for the spatial sampling of an optical wavefront. The other is that the computational treatment of images has become accessible largely, which has benefited from the significant improvement in microprocessor performance, in particular their processing units as well as storage capacities. Due to the high-frequency oscillation of visible light wavefront, Conventional optical detectors only respond to the intensity or amplitude of the incident light. Only the intensity-value measurement in the real-domain can be recorded by the camera from the mathematics. Holographic imaging becomes the necessary link with the help of additional optical configurations and computational algorithms. After decades of development, multiple branches were multiplied with the simultaneous development of optical measurement technology and computer technology. The development of holographic imaging has been discussed in the context of these solutions, focusing on the principal approaches that have had a significant impact on modern holographic methods and applications: digital holography, optical diffraction tomography, phase shifting interference, phase retrieval, holographic multiplexing, multiple model and deep learning.Interference technology has played an important role in the field of optical measurement. By introducing the reference wave, the invisible phase information is transformed into the interference fringe distribution. A series of fringe analysis and reconstruction algorithms are used to demodulate the phase from the interferogram. The most classic fringe analysis is phase-shifting interferometry. When the interference angle of the reference wave becomes large, the interference fringe is equivalent to the high-frequency carrier, and the object information is encoded into the high spatial frequency domain. The complex amplitude of the object can be extracted, which is the mainstream method of holographic imaging. The spatial frequency distribution of the image is 2D, which can introduce interference in different spatial directions, thus inspiring the birth of holographic multiplexing.Different from interferometry, another series of methods is based on wave diffraction with non-interferometry. the intensity distribution of the diffraction field of the object is recorded, then the complex-amplitude of the object is reconstructed from the diffraction field. This process can be considered as a mathematical inverse problem, that is phase retrieval. The advantage of non-interferometry is that it can further simplify the optical system, and transform the “burden” of the configuration to the calculation. With the development of computer processing power, deep neural networks have become a research hotspot in solving inverse problems in imaging. The diffraction intensity is associated with the measured wavefront through numerical diffraction with neural networks, which can replace traditional holography to achieve functions such as digital focusing, phase unwrapping, and label-free virtual dyeing.Thanks to the advancements in detecting devices, laser sources, and computing powers, there have been experimentally significant technical advances in holographic imaging. The applications have been expanded to various fields, from biophysics, cell biology, hematology, to infectious diseases.