A new type of Mobile Ad Hoc Network (MANET) is Vehicular Ad Hoc Network (VANET) that allows smart transport system to provide road security and reduce traffic jam through automobile to automobile and automobile to roadside communication. However, security issues for VANETs have become a major concern for researchers. VANET is different from other ad hoc networks due to its dynamic topology and mixed structural design. Hence, designing security schemes to authenticate broadcasted messages and discard malicious messages are crucial in VANETs. Here, at first we identify various security issues for VANET and discuss possible defense mechanisms to mitigate those threats. We then classify the defense mechanisms into major categories and critically analyze them based on different performance criteria. Finally, we list several open research issues related to VANET security to inspire researchers to work on these open problems and propose solutions towards efficient trust organization in VANET.