Light field imaging has emerged as a technology allowing to capture richer visual information from our world. As opposed to traditional photography, which captures a 2D projection of the light in the scene integrating the angular domain, light fields collect radiance from rays in all directions, demultiplexing the angular information lost in conventional photography. On the one hand, this higher-dimensional representation of visual data offers powerful capabilities for scene understanding, and substantially improves the performance of traditional computer vision problems such as depth sensing, post-capture refocusing, segmentation, video stabilization, material classification, etc. On the other hand, the high-dimensionality of light fields also brings up new challenges in terms of data capture, data compression, content editing and display. Taking these two elements together, research in light field image processing has become increasingly popular in the computer vision, computer graphics and signal processing communities. In this article, we present a comprehensive overview and discussion of research in this field over the past 20 years. We focus on all aspects of light field image processing, including basic light field representation and theory, acquisition, super-resolution, depth estimation, compression, editing, processing algorithms for light field display, and computer vision applications of light field data. Index Terms-Light field imaging, light field processing.