Connected and fully automated vehicles are expected to revolutionize our mobility in the near future on a global scale, by significantly improving road safety, traffic efficiency, and traveling experience. Enhanced vehicular applications, such as cooperative sensing and maneuvering or vehicle platooning, heavily rely on direct connectivity among vehicles, which is enabled by sidelink communications. In order to set the ground for the core contribution of this paper, we first analyze the main streams of the cellular-vehicle-to-everything (C-V2X) technology evolution within the Third Generation Partnership Project (3GPP), with focus on the sidelink air interface. Then, we provide a comprehensive survey of the related literature, which is classified and critically dissected, considering both the Long-Term Evolution-based solutions and the 5G New Radio-based latest advancements that promise substantial improvements in terms of latency and reliability. The wide literature review is used as a basis to finally identify further challenges and perspectives, which may shape the C-V2X sidelink developments in the next-generation vehicles beyond 5G.