Multidimensional optical imaging systems for information processing and visualization technologies have numerous applications in fields such as manufacturing, medical sciences, entertainment, robotics, surveillance, and defense. Among different three-dimensional (3-D) imaging methods, integral imaging is a promising multiperspective sensing and display technique. Compared with other 3-D imaging techniques, integral imaging can capture a scene using an incoherent light source and generate real 3-D images for observation without any special viewing devices. This review paper describes passive multidimensional imaging systems combined with different integral imaging configurations. One example is the integral-imaging-based multidimensional optical sensing and imaging systems (MOSIS), which can be used for 3-D visualization, seeing through obscurations, material inspection, and object recognition from microscales to long range imaging. This system utilizes many degrees of freedom such as time and space multiplexing, depth information, polarimetric, temporal, photon flux and multispectral information based on integral imaging to record and reconstruct the multidimensionally integrated scene. Image fusion may be used to integrate the multidimensional images obtained by polarimetric sensors, multispectral cameras, and various multiplexing techniques. The multidimensional images contain substantially more information compared with two-dimensional (2-D) images or conventional 3-D images. In addition, we present recent progress and applications of 3-D integral imaging including human gesture recognition in the time domain, depth estimation, mid-wave-infrared photon counting, 3-D polarimetric imaging for object shape and material identification, dynamic integral imaging implemented with liquid-crystal devices, and 3-D endoscopy for healthcare applications.