It is expected that the number of drones used in both commercial and leisure operations will grow significantly in the coming years, which raises the need for a solid framework for management of this traffic. Unmanned traffic management (UTM) is a system for handling autonomous drone flights over urban areas. This thesis addresses the central questions in UTM: how much traffic is sustainable in a city scenario and what are the possible ways of managing the flights. We consider both horizontal-maneuver collision avoidance and vertical deconfliction strategies, including risk management solutions inspired by performance-based navigation (PBN) - a unifying theme for ongoing airspace modernization efforts (we also consider traffic management for the conventional, manned aviation). We use mathematical modeling and conduct numerical simulations to obtain capacity estimations for a geographical area and present algorithms for airspace management. To our knowledge this is the first thesis on UTM, and several directions for future research are also identified.