Cooperative Intelligent Transportation Systems, mainly represented by vehicular ad hoc networks (LTE-As), are among the key components contributing to the Smart City and Smart World paradigms. Based on the continuous exchange of both periodic and event triggered messages, smart vehicles can enhance road safety, while also providing support for comfort applications. In addition to the different communication protocols, securing such communications and establishing a certain trustiness among vehicles are among the main challenges to address, since the presence of dishonest peers can lead to unwanted situations. To this end, existing security solutions are typically divided into two main categories, cryptography and trust, where trust appeared as a complement to cryptography on some specific adversary models and environments. Where the latter was not enough to mitigate all possible attacks. In this paper, we provide an adversary-oriented survey of the existing trust models for LTE-As. We also show when trust is preferable to cryptography, and the opposite. In addition, we show how trust models are usually evaluated in LTE-A contexts, and finally, we point out some critical scenarios that existing trust models cannot handle, together with some possible solutions.