Computational imaging breaks the limitation of traditional digital imaging to acquire the information deeper (e.g., high dynamic range imaging and low light imaging) and broader (e.g., spectrum, light field, and 3D imaging). Driven by industry, especially mobile phone manufacturer medical and automotive, computational imaging has become ubiquitous in our daily lives and plays a critical role in accelerating the revolution of industry. It is a new imaging technique that combines illumination, optics, image sensors, and post-processing algorithms. This review takes the latest methods, algorithms, and applications as the mainline and reports the state-of-the-art progress by jointly analyzing the articles and reports at home and aboard. This review covers the topics of end-to-end optics and algorithms design, high dynamic range imaging, light-field imaging, spectrum imaging, lensless imaging, low light imaging, 3D imaging, and computational photography. It focuses on the development status, frontier dynamics, hot issues, and trends in each computational imaging topic. The camera systems have long-term been designed in separated steps: experience-driven lens design followed by costume designed post-processing. Such a general-propose approach achieved success in the past but left the question open for specific tasks and the best compromise among optics, post-processing, and costs. Recent advances aim to build the gap in an end-to-end fashion. To realize the joint optics and algorithms designing, different differentiable optics models have been realized step by step, including the differentiable diffractive optics model, the differentiable refractive optics, and the differentiable complex lens model based on differentiable ray-tracing. Beyond the goal of capturing a sharp and clear image on the sensor, it offers enormous design flexibility that can not only find a compromise between optics and post-processing, but also open up the design space for optical encoding. The end-to-end camera design offers competitive alternatives to modern optics and camera system design. High dynamic range (HDR) imaging has become a commodity imaging technique as evidenced by its applications across many domains, including mobile consumer photography, robotics, drones, surveillance, content capture for display, driver assistance systems, and autonomous driving. This review analyzes the advantages, disadvantages, and industrial applications through analyzing a series of HDR imaging techniques, including optical modulation, multi-exposure, multi-sensor fusion, and post-processing algorithms. Conventional cameras do not record most of the information about the light distribution entering from the world. Light-field imaging records the full 4D light field measuring the amount of light traveling along each ray that intersects the sensor. This review reports how the light field is applied to super-resolution, depth estimation, 3D measurement, and so on and analyzes the state-of-the-art method and industrial application. It also reports the research progress and industrial application in particle image velocimetry and 3D flame imaging. Spectral imaging technique has been used widely and successfully in resource assessment, environmental monitoring, disaster warning, and other remote sensing domains. Spectral image data can be described as a three-dimensional cube. This imaging technique involves capturing the spectrum for each pixel in an image; As a result, the digital images produce detailed characterizations of the scene or object. This review explains multiple methods to acquire spectrum volume data, including the current multi-channel filter, solving the wavelength response curve inversely based on deep learning, diffraction grating, multiplexing, metasurface, and other optimizations to achieve hyper-spectrum acquisition. Lensless imaging eliminates the need for geometric isomorphism between a scene and an image while constructing compact and lightweight imaging systems. It has been applied to bright-field imaging, cytometry, holography, phase recovery, fluorescence, and the quantitative sensing of specific sample properties derived from such images. However, the low reconstructed signal-to-noise ratio makes it an unsolved challenging inverse problem. This review reports the recent progress in designing and optimizing planar optical elements and high-quality image reconstruction algorithms combined with specific applications. Imaging under a low light illumination will be affected by Poisson noise, which becomes increasingly strong as the power of the light source decreases. In the meantime, a series of visual degradation like decreased visibility, intensive noise, and biased color will occur. This review analyzes the challenges of low light imaging and conclude the corresponding solutions, including the noise removal methods of single/multi-frame, flash, and new sensors to deal with the conditions when the sensor exposure to low light. Shape acquisition of three-dimensional objects plays a vital role for various real-world applications, including automotive, machine vision, reverse engineering, industrial inspections, and medical imaging. This review reports the latest active solutions which have been widely applied, including structured light, direct time-of-flight, and indirect time-of-flight. It also notes the difficulties like ambient light (e.g., sunlight), indirect inference (e.g., the mutual reflection of the concave surface, scattering of foggy) of depth acquisition based on those active methods. The use of computation methods in photography refers to digital image capture and processing techniques that use digital calculation instead of optical processes. It can not only improve the camera ability but also add more new features that were not possible at all with traditional film-based photography. Computational photography is an essential branch of computation imaging developed from traditional photography - however, computational photography emphasizes taking a photograph digitally. Limited by the physical size and image quality, computational photography focuses on reasonably arranging the computational resources and showing the high-quality image that pleasures the customer's feeling. As 90 percent of the information transmitted to our human brain is visual, the imaging system plays a vital role for most future intelligence systems. Computational imaging drastically releases human information acquisition ability in no matter depth or scope. For new techniques like metaverse, computational imaging offers a general input tool to collect multi-dimensional visual information for rebuilding the virtual world. This review covers key technological developments, applications, insights, and challenges over the recent years and examines current trends to predict future capabilities.