Tensor displays are a family of glasses-free 3D displays comprising all architectures employing (a stack of) time-multiplexed LCDs illuminated by uniform or directional backlighting. We introduce a unified optimization framework that encompasses all tensor display architectures and allows for optimal glasses-free 3D display. We demonstrate the benefits of tensor displays by constructing a reconfigurable prototype using modified LCD panels and a custom integral imaging backlight. Our efficient, GPU-based NTF implementation enables interactive applications. In our experiments we show that tensor displays reveal practical architectures with greater depths of field, wider fields of view, and thinner form factors, compared to prior automultiscopic displays.