Vehicular Ad-hoc Networks (VANETs) are specialized type of Mobile Ad-hoc Networks (MANETs) developed to support vehicle-to-vehicle and vehicle-to-infrastructure communication. Security threats in these networks include malicious nodes, Man-in-the-Middle (MitM) attacks and Denial of Service (DoS) attacks which threaten network reliability. Trust-based models in VANETS seek to evaluate trust of nodes and data sharedand incorporate certain features which enhance adaptivity. This systematic literature review (SLR) analyses the adaptive trust-based models available in VANETs with an emphasis on the features that facilitate adaptability in the dynamic environment. The review follows Barbara Kitchenham (2007) systemic approach and accesses databases including Google Scholar, IEEE Xplore and Wiley Online Library where 34 articles are included. The findings highlight important characteristics such as historic data analysis, real-time behavior monitoring, adaptive trust score update, frequency of messages, context awareness and real-time detection of intrusive attacks that make the VANETs trust models more adaptable.