  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.
