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Graphene is a promising materials platform for metasurface flat optics at terahertz wavelengths, with the important advantage of active tunability. Here we review recent work aimed at the development of tunable graphene metasurfaces for THz wavefront shaping (including beam-steering metamirrors and metalenses) and light emission. Various design strategies for the constituent meta-units are presented, ranging from metallic phase-shifting elements combined with a nearby graphene sheet for active tuning to graphene plasmonic resonators providing the required phase control or radiation mechanism. The key challenge in the development of these devices, related to the limited radiative coupling of graphene plasmonic excitations, is discussed in detail together with recently proposed solutions. The resulting metasurface technology can be expected to have a far-reaching impact on a wide range of device applications for THz imaging, sensing, and future wireless communications.