The deployment of future Internet and communication technologies (ICT) provide intelligent transportation systems (ITS) with huge volumes of real-time data (Big Data) that need to be managed, communicated, interpreted, aggregated and analysed. These technologies considerably enhance the effectiveness and user friendliness of ITS, providing considerable economic and social impact. Real-world application scenarios are needed to derive requirements for software architecture and novel features of ITS in the context of the Internet of Things (IoT) and cloud technologies. In this study, we contend that future service- and cloud-based ITS can largely benefit from sophisticated data processing capabilities. Therefore, new Big Data processing and mining (BDPM) as well as optimization techniques need to be developed and applied to support decision-making capabilities. This study presents real-world scenarios of ITS applications, and demonstrates the need for next-generation Big Data analysis and optimization strategies. Decentralised cooperative BDPM methods are reviewed and their effectiveness is evaluated using real-world data models of the city of Hannover, Germany. We point out and discuss future work directions and opportunities in the area of the development of BDPM methods in ITS.