Security issues have always posed a major threat and challenge to the Internet of Things (IoTs), especially the vehicular ad-hoc networks (VANETs), a subcategory of IoTs in the automotive field. The traditional methods to solve these ever-growing security issues in VANETs are mainly cryptography-based. As an effective and efficient complement to those solutions, trust management solutions and reputation models have been widely explored to deal with malicious or selfish vehicle intrusion and forged data spoofing, with the aim of enhancing the overall security, reliability, trustworthiness, and impartiality of VANETs. For the integrity of the article, this survey begins with providing the background information of VANETs, including the basic components and general architecture. Then, many attacks in VANETs are investigated, analyzed, and compared to understand the functional relevance of the following trust and reputation methods. Various approaches offer various countermeasures against these types of attacks. At the same time, the latest development of emerging technologies such as blockchain, software-defined network, and cloud computing opens up new possibilities for more and more promising trust and reputation management models and systems in VANETs. After that, the survey reviews the most important trust and reputation models and schemes which are widely mentioned in the literature based on our developed technique-based taxonomy, in contrast to the popular “entity-centric, data-centric, hybrid” taxonomy in the field, to adapt to the recent technological development of these management schemes in VANETs. Finally, discussions and speculations on the future direction of research into the trust and reputation management in VANETs are presented.