Vehicular ad hoc networks (VANETs) provide the potential to improve transportation efficiency by facilitating the sharing of traffic information among vehicles. Acceptance of VANET depends on communication speed and accuracy as well as privacy protection guaranteeing an individual's safety. Vehicle authentication is necessary to ensure message correctness. This necessitates the implementation of an effective privacy-preserving authentication scheme, as well as the need for both secrecy and timebound delivery of messages. Various privacy-preserving authentication schemes have been suggested to guarantee the integrity of messages in communications. However, most of the schemes are not able to solve issues related to computing costs, communication, security, privacy, threats, and vulnerabilities. In this review, we focus on cryptographic strategies that are suggested to accomplish privacy and authentication, such as identity-based, public key cryptography-based, pseudonym-based, and blockchain-based schemes. We provide a thorough analysis of schemes, including their categorizations, advantages, and drawbacks. The study demonstrates that the majority of current authentication techniques necessitate trusted authorities that lack transparency in their operations. Additionally, authentication process incurs substantial computational and communication overhead, leading to a considerable impact on the timely delivery of messages. More efforts are required to enhance the development of efficient authentication schemes in VANETs.