Expected to operate in the imminent future, air taxi service (ATS) is an aerial on-demand transport for a single passenger or a small group of riders, which seeks to transform the method of everyday commute. This uncharted territory in the emerging transportation world is anticipated to enable consumers bypass traffic congestion in urban road networks. By adopting an electric vertical takeoff and landing concept (eVTOL), air taxis could be operational from skyports retrofitted on building rooftops, thus gaining advantage from an implementation standpoint. Motivated by the potential impact of ATS, this study provides a review of air taxi systems and associated operations. We first discuss the current developments in the ATS (demand prediction, air taxi network design, and vehicle configuration). Next, we anticipate potential future challenges of ATS from an operations management perspective, and review the existing literature that could be leveraged to tackle these problems (ride-matching, pricing strategies, vehicle maintenance scheduling, and pilot training and recruitment). Finally, we detail future research opportunities in the air taxi domain.