Glasses-free three-dimensional (3D) display is the gateway to the “metaverse” and it is a transformative technology that can redefine the way human interact with information. After more than a hundred years’ development, glasses-free 3D display has made significant progress, but there are still a bunch of problems, such as limited field of view (FOV), severe resolution degradation, limited movement parallax and visual fatigue. Recent studies have shown that micro/nano photonic devices (diffractive gratings, diffractive lens and metasurfaces) have flexible and accurate manipulating capability on the intensity, phase, polarization and other parameters of lightwave. It is expected that nanophotonics can solve the intrinsic bottleneck of glasses-free 3D display. However, micro-nano photonic devices face significant challenges at both the design and fabrication levels. In this paper, the limitations of glasses-free 3D display based on geometric optics are analyzed, and the latest research progress of glasses-free 3D display based on planar optics is introduced in detail from the aspects of device design and micro-nano fabrication. Finally, we highlight the future direction and potential applications of glasses-free 3D display.