We introduce tensor displays: a family of compressive light field displays comprising all architectures employing a stack of timemultiplexed, light-attenuating layers illuminated by uniform or directional backlighting (i.e., any low-resolution light field emitter). We show that the light field emitted by an N-layer, M-frame tensor display can be represented by an Nth -order, rank-M tensor. Using this representation we introduce a unified optimization framework, based on nonnegative tensor factorization (NTF), encompassing all tensor display architectures. This framework is the first to allow joint multilayer, multiframe light field decompositions, significantly reducing artifacts observed with prior multilayer-only and multiframe-only decompositions; it is also the first optimization method for designs combining multiple layers with directional backlighting. We verify the benefits and limitations of tensor displays by constructing a prototype using modified LCD panels and a ...