Three-dimensional (3-D) optical image sensing and visualization technologies have been researched extensively for different applications in fields as diverse as entertainment, medical sciences, robotics, manufacturing, and defense. In many instances, the capabilities of 3-D imaging and display systems have revolutionized the progress of these disciplines, enabling new detection/display abilities that would not have been otherwise possible. As one of the promising methods in the area of 3-D sensing and display, integral imaging offers passive and relatively inexpensive way to capture 3-D information and to visualize it optically or computationally. The integral imaging technique belongs to the broader class of multiview imaging techniques and is based on a century old principle which has only been resurrected in the past decade owing to advancement of optoelectronic image sensors as well as the exponential increase in computing power. In this paper, historic and physical foundations of integral imaging are overviewed; different optical pickup and display schemes are discussed and system parameters and performance metrics are described. In addition, computational methods for reconstruction and range estimation are presented and several applications including 3-D underwater imaging, near infra red passive sensing, imaging in photon-starved environments, and 3-D optical microscopy are discussed among others.