The capture and display of images of 3-D scenes under incoherent and polychromatic illumination is currently a hot topic of research, due to its broad applications in bioimaging, industrial procedures, military and surveillance, and even in the entertainment industry. In this context, Integral Imaging (InI) is a very competitive technology due to its capacity for recording with a single exposure the spatial-angular information of light-rays emitted by the 3-D scene. From this information, it is possible to calculate and display a collection of horizontal and vertical perspectives with high depth of field. It is also possible to calculate the irradiance of the original scene at different depths, even when these planes are partially occluded or even immersed in a scattering medium. In this paper, we describe the fundaments of InI and the main contributions to its development. We also focus our attention on the recent advances of the InI technique. Specifically, the application of InI concept to microscopy is analyzed and the achievements in resolution and depth of field are explained. In a different context, we also present the recent advances in the capture of large scenes. The progresses in the algorithms for the calculation of displayable 3-D images and in the implementation of setups for the 3-D displays are reviewed.