Since the development of transport systems, humans have exploited ground-level, below-ground, and high-altitude spaces for transportation purposes. However, with the increasing burden of expanding populations and rapid urbanization in recent decades, public transportation systems and freight traffic are suffering huge pressure, plaguing local governments, and straining economies. Engineers and researchers have started to re-examine, propose, and develop the underused near-ground spaces (NGS) for transportation purposes. For instance, flying cars, which are not a totally novel idea, aim at solving the traffic congestion problem and releasing the strains on existing city transport networks by utilizing unoccupied NGS. This paper aims to describe the modern advances, techniques, and challenges of FCTS. Additionally, since large-scale operations of flying cars can improve current transportation problems, we also introduce different facets of the various designs of FCTS, including path and trajectory planning, supporting facilities, and commercial designs. Finally, we discuss the challenges that might arise while developing and commercializing FCTS in terms of safety issues, commercial issues, and ethical issues.