Holography is a kind of technique enabling 3D imaging which has been applied in many practical fields. With the rapid development of computer science and technology, computer generated holography (CGH) has become a common holography design method due to its high convenience and flexibility. Herein, we present a review of our recent progress in metasurface-based terahertz CGH. In these demonstrations, the metasurfaces acting as the holograms have shown the novel capabilities beyond the conventional counterparts. We first present a meta-hologram with simultaneous and independent phase and amplitude control over each pixel, which enables high-quality holographic imaging. Such new characteristic also predicts new holographic imaging performances including holographic images transforming continuously along the propagation direction realized by dielectric metasurface. Then different responses under different incident polarization states are designed. A linear polarization and frequency multiplexed meta-hologram, a reflective circular polarization multiplexed meta-hologram, and a surface-wave-based polarization multiplexed meta-hologram have been achieved respectively. Furthermore, a thermally dependent dynamic meta-hologram which can change the holographic image actively is also given. The proposed method paves a novel way to the design and realization of CGH functional devices in the future and contributes to the development of metasurfaces towards practical applications.