Holography has attracted tremendous interest due to its capability of storing both the amplitude and phase of light field and reproducing vivid three-dimensional scenes. However, the large pixel size, low resolution, small field-of-view (FOV) and limited space-bandwidth of traditional spatial light modulator (SLM) devices restrict the possibility of improving the quality of reconstructed images. With the development of nanofabrication technologies, metasurfaces have shown great potential in manipulating the amplitude, phase, polarization, frequency or simultaneously multiple parameters of output light in ultrashort distance with subwavelength resolution by tailoring the scattering behaviour of consisted nanostructures. Such flexibilities make metasurface a promising candidate for holographic related applications. Here, we review recent progresses in the field of metasurface holography. From the perspective of the fundamental properties of light, we classify the metasurface holography into several categories such as phase-only holography, amplitude-only holography, complex amplitude holography and so on. Then, we introduce the corresponding working principles and design strategies. Meanwhile, some emerging types of metasurface holography such as tunable holography, nonlinear holography, Janus (or directional related) and bilayer metasurfaces holography are also discussed. At last, we make our outlook on metasurface holography and discuss the challenges we may face in the future.