Holography has emerged as a vital approach to fully engineer the wavefronts of light since its invention dating back to the last century. However, the typically large pixel size, small field of view and limited space-bandwidth impose limitations in the on-demand high-performance applications, especially for three-dimensional displays and large-capacity data storage. Meanwhile, metasurfaces have shown great potential in controlling the propagation of light through the well-tailored scattering behavior of the constituent ultrathin planar elements with a high spatial resolution, making them suitable for holographic beam-shaping elements. Here, we review recent developments in the field of metasurface holography, from the classification of metasurfaces to the design strategies for both free-space and surface waves. By employing the concepts of holographic multiplexing, multiple information channels, such as wavelength, polarization state, spatial position and nonlinear frequency conversion, can be employed using metasurfaces. Meanwhile, the switchable metasurface holography by the integration of functional materials stimulates a gradual transition from passive to active elements. Importantly, the holography principle has become a universal and simple approach to solving inverse engineering problems for electromagnetic waves, thus allowing various related techniques to be achieved.