Different from traditional transport systems, such as cars or trains, which are limited by land transit space, flying cars (such as UAS, drones, and air taxis) do not occupy space with traffic. They have a degree of freedom in space and time, smaller displacement, and consequently, less stress for their users. Large companies and researchers around the world are working with different architectures, algorithms, and techniques to test air taxi transport to serve a significant proportion of people safely and autonomously. One of the main issues surrounding the diffusion of air taxis is safety and security, since a simple failure can lead to the loss of high-value assets, loss of the vehicle, and/or injuries to human lives, including fatalities. In this sense, despite significant efforts, the literature is still specific and limited regarding air taxi safety and security. Therefore, this study aimed to carry out an extensive systematic literature review of the main modern advances in techniques, architectures, and research carried out around the world focused on these types of vehicles. More than 210 articles from between 2015 and January 2022 were individually reviewed. In addition, this study also presents gaps that could serve as a direction for future research. As far as the authors are aware, no other study performs this type of review focused on air taxi safety.