Abstract Benefiting from the prominent performance in high-density information storage and fast accessing of two-dimensional data, holography has attracted tremendous attentions. The wavefront recording of traditional holographic devices such as diffraction optical elements suffers from the design complexity and poor resolution as it relies on phase accumulation in the propagating mode, which is achieved by gradually varying the refractive index or thickness of the medium. Ultrathin metasurfaces made of engineered meta-atoms can overcome these limitations owing to their outstanding design flexibility and subwavelength thicknesses. In contrast to the traditional bulky holographic components, the performance of metasurfaces is determined by the electromagnetic response of the meta-atoms with spatially varying in-plane geometric parameters or rotation angles, which enables them to flexibly control the phase, amplitude, wavelength, and polarization of electromagnetic wave. Because of the design flexibility and the capacity of arbitrary wavefront manipulation, metasurfaces are emerging as a promising candidate for holographic memory systems. Here, we review the fast-growing field of metasurface holograms from design principles to recent advances in microwave regime. At the end of the review, we discuss potential applications of the metasurface holography and present a future research outlook.