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In order to fulfill transportation demands, people have well-explored ground, waterborne, and high-altitude spaces (HAS) for transportation purposes, as well as the underground space under cities (namely, subway systems). However, due to the increased burdens of population and urbanization in recent decades, huge pressures on public transportation and freight traffic are introduced to cities, plaguing the governors and constraining the development of economics. By observing the fact that near-ground space (NGS) has rarely been utilized, researchers and practitioners started to re-examine, propose and develop flying cars, which are not a totally novel idea, aiming at solving the traffic congestion problem and releasing the strains of cities. Flying cars completely differ from traditional grounded transportation systems, where automobiles/trains are suffering track limitations and are also different from the air flights in HAS for long-distance transfer. Therefore, while observing the lack of specific literature on flying cars and flying car transportation systems (FCTS), this paper is motivated to study the advances, techniques, and challenges of FCTS imposed by the inherent nature of NGS transportation and to devise useful proposals for facilitating the construction and commercialization of FCTS, as well as to facilitate the readers understanding of the incoming FCTS. We first introduce the increased requirements for transportation and address the advantages of flying cars. Next, a brief overview of the developing history of flying cars is presented in view of both timeline and technique categories. Then, we discuss and compare the state of the art in the design of flying cars, including take-off \& landing (TOL) modes, pilot modes, operation modes, and power types, which are respectively related to the adaptability, flexibility & comfort, stability & complexity, environmental friendliness of flying cars. Additionally, since large-scale operations of flying cars can improve the aforementioned transportation problem, we also introduce the designs of FCTS, including path and trajectory planning, supporting facilities and commercial designs. Finally, we discuss the challenges which might be faced while developing and commercializing FCTS from three aspects: safety issues, commercial issues, and ethical issues.