Vehicle-to-everything (V2X), including vehicle- to-vehicle (V2V), vehicle-to-pedestrian (V2P), vehicle-to-infrastructure (V2I), and vehicle-to-network (V2N) communications, improves road safety, traffic efficiency, and the availability of infotainment services. Standardization of Long Term Evolution (LTE)-based V2X has been actively conducted by the Third Generation Partnership Project (3GPP) to provide solutions for V2X communications, and has benefited from the global deployment and fast commercialization of LTE systems. LTE-based V2X was widely used as LTE-V in the Chinese vehicular communications industry, and LTE-based V2X was redefined as LTE V2X in 3GPP standardization progress. In this article, the overview of requirements and use cases in V2X services in 3GPP is presented. The up-to-date standardization of LTE V2X in 3GPP is surveyed. The challenges and detailed design aspects in LTE V2X are also discussed. Meanwhile, the enhanced V2X (eV2X) services and possible 5G solutions are analyzed. Finally, the implementations of LTE V2X are presented with the latest progress in industrial alliances, research, development of prototypes, and field tests.