Compressive image acquisition and display is an emerging architecture for consumer electronics that explores the co-design of optics, electronics, applied mathematics, and real-time computing. Together, these hardware/software systems exploit compressibility of the recorded or presented data to facilitate new device form factors and relax requirements on electronics and optics. For instance, light field or glasses-free 3D displays usually show different perspectives of the same 3D scene to a range of different viewpoints. All these images are very similar and therefore highly compressible. By combining multilayer hardware architectures and directional backlighting with real-time implementations of light field tensor factorization, limitations of existing displays, for instance in resolution, contrast, depth of field, and field of view, can be overcome. A similar design paradigm also applies to light field and multi-spectral image acquisition, super-resolution and high dynamic range display, glasses-free 3D projection, computational lithography, microscopy, and many other applications. In this talk, we review the fundamentals of compressive camera and display systems and discuss their impact on future consumer electronics, remote sensing, scientific imaging, and human-computer interaction.