In general relativity, astrophysical black holes are characterized uniquely in terms of their masses and spins and are described by the Kerr metric. The high sensitivity and resolution of the EHT will allow for unprecedented tests of the Kerr nature of black holes and, hence, of general relativity. I will present current and future limits on deviations from the Kerr metric from Sgr A* in the context of radiatively-inefficient accretion flow models. I will also show how largely model-independent constraints on such deviations can be obtained from the angular diameter of the photon ring of Sgr A* in combination with existing mass and distance measurements. Finally, I will describe a new general framework for the parametrization of deviations from the Kerr metric.