The article brings together the academic and industry literature on the design and management of urban airspace. We analyze the proposed airspace concepts, identify their strengths and weaknesses, point to gaps in research, and provide recommendations for a more holistic approach to designing urban airspace. We first identify the structural factors that define the size, capacity, and geometry of urban airspace. These factors are grouped into four categories: safety-related factors, social factors, system factors, and aircraft factors. Second, we review different urban airspace concepts proposed around the world. Third, we assess the airspace concepts based on the identified factors. Most of the reviewed airspace concepts are idealized as abstract networks, with an emphasis on maximizing safety and capacity, and with little regard for factors such as technological complexity, noise, or privacy. Additionally, we find that the airspace structure directly influences the level of safety, efficiency, and capacity of airspace. On the one hand, air vehicles in less structured airspace have more degrees of freedom. They can freely choose their position, altitude, heading, and speed, which increases airspace capacity and reduces flying costs. However, these concepts require high technological capabilities, such as dynamic geofences and advanced sense-and-avoid capabilities, to maintain the required safety levels. On the other hand, airspace concepts with fewer degrees of freedom can accommodate less capable aircraft but require strict operation rules and reduced capacity to ensure safety. Finally, the proposed urban air mobility concepts require extensive ground infrastructures, such as take-off and landing pads and communication, navigation, and surveillance infrastructure. There is a need for a new branch of research that analyzes urban air mobility from the perspective of urban planning, including issues around zoning, air rights, public transportation, real estate development, public acceptance, and access inequalities.