Recent advances in smart connected vehicles and Intelligent Transportation Systems (ITS) are based upon the capture and processing of large amounts of sensor data. Modern vehicles contain many internal sensors to monitor a wide range of mechanical and electrical systems and the move to semi-autonomous vehicles adds outward looking sensors such as cameras, lidar, and radar. ITS is starting to connect existing sensors such as road cameras, traffic density sensors, traffic speed sensors, emergency vehicle, and public transport transponders. This disparate range of data is then processed to produce a fused situation awareness of the road network and used to provide real-time management, with much of the decision making automated. Road networks have quiet periods followed by peak traffic periods and cloud computing can provide a good solution for dealing with peaks by providing offloading of processing and scaling-up as required, but in some situations latency to traditional cloud data centres is too high or bandwidth is too constrained. Cloud computing at the edge of the network, close to the vehicle and ITS sensor, can provide a solution for latency and bandwidth constraints but the high mobility of vehicles and heterogeneity of infrastructure still needs to be addressed. This paper surveys the literature for cloud computing use with ITS and connected vehicles and provides taxonomies for that plus their use cases. We finish by identifying where further research is needed in order to enable vehicles and ITS to use edge cloud computing in a fully managed and automated way. We surveyed 496 papers covering a seven-year timespan with the first paper appearing in 2013 and ending at the conclusion of 2019.