In this talk, we explore modern approaches to glasses-free 3D display using compressive light field displays. In contrast to conventional technology, compressive displays aim for a joint-design of optics, electronics, and computational processing that together exploit compressibility of the presented data. For instance, multiview images or light fields show the same 3D scene from different perspectives - all these images are very similar and therefore compressible. By combining displays that use multilayer architectures or directional backlighting combined with optimal light field factorizations, limitations of existing devices, for instance resolution, depth of field, and field of view, can be overcome. In addition to light field display, we will discuss approaches to compressive super-resolution image display and compressive high dynamic range display. As with compressive light field displays, these technologies rely on multiplexing image content in time such that the visual system of a human observer combines presented patterns into a consistent 3D, high-resolution, or high-contrast image. With the invention of integral imaging and parallax barriers in the beginning of the 20th century, glasses-free 3D displays have become feasible. With rapid advances in optical fabrication, digital processing power, and computational perception, a new generation of display technology is emerging: compressive displays exploring the co-design of optical elements and computational processing while taking particular characteristics of the human visual system into account. We will review these techniques and also give an outlook on next-generation compressive light field camera technology.