Urban Air Mobility (UAM) involving piloted or autonomous aerial vehicles, is envisioned as emerging disruptive technology for next-generation transportation addressing mobility challenges in congested cities. This paradigm may include aircrafts ranging from small unmanned aerial vehicles (UAVs) or drones, to aircrafts with passenger carrying capacity, such as personal air vehicles (PAVs). This paper highlights the UAM vision and brings out the underlying fundamental research challenges and opportunities from computing, networking, and service perspectives for sustainable design and implementation of this promising technology providing an innovative infrastructure for urban mobility. Important research questions include, but are not limited to, real-Time autonomous scheduling, dynamic route planning, aerial-To-ground and inter-vehicle communications, airspace traffic management, on-demand air mobility, resource management, quality of service and quality of experience, sensing (edge) analytics and machine learning for trustworthy decision making, optimization of operational services, and socio-economic impacts of UAM infrastructure on sustainability.