With the popularization of positioning devices such as GPS navigators and smart phones, large volumes of spatiotemporal trajectory data have been produced at unprecedented speed. For many trajectory mining problems, a number of computationally efficient approaches have been proposed. However, to more effectively tackle the challenge of big data, it is important to exploit various advanced parallel computing paradigms. In this paper, we present a comprehensive survey of the state-of-the-art techniques for mining massive-scale spatiotemporal trajectory data based on parallel computing platforms such as Graphics Processing Unit (GPU), MapReduce and Field Programmable Gate Array (FPGA). This survey covers essential topics including trajectory indexing and query, clustering, join, classification, pattern mining and applications. We also give an in-depth analysis of the related techniques and compare them according to their principles and performance.