Due to the growing number of vehicles on the roads worldwide, road traffic accidents are currently recognized as a major public safety problem. In this context, connected vehicles are considered as the key enabling technology to improve road safety and to foster the emergence of next generation cooperative intelligent transport systems (ITS). Through the use of wireless communication technologies, the deployment of ITS will enable vehicles to autonomously communicate with other nearby vehicles and roadside infrastructures and will open the door for a wide range of novel road safety and driver assistive applications. However, connecting wireless-enabled vehicles to external entities can make ITS applications vulnerable to various security threats, thus impacting the safety of drivers. This article reviews the current research challenges and opportunities related to the development of secure and safe ITS applications. It first explores the architecture and main characteristics of ITS systems and surveys the key enabling standards and projects. Then, various ITS security threats are analyzed and classified, along with their corresponding cryptographic countermeasures. Finally, a detailed ITS safety application case study is analyzed and evaluated in light of the European ETSI TC ITS standard. An experimental test-bed is presented, and several elliptic curve digital signature algorithms (ECDSA) are benchmarked for signing and verifying ITS safety messages. To conclude, lessons learned, open research challenges and opportunities are discussed.