In the era of big data, there has been a surge in the availability of data containing rich spatial and temporal information, offering valuable insights into dynamic systems and processes for applications such as weather forecasting, natural disaster management, intelligent transport systems, and precision agriculture. Graph neural networks (GNNs) have emerged as a powerful tool for modeling and understanding data with dependencies to each other such as spatial and temporal dependencies. There is a large amount of existing work that focuses on addressing the complex spatial and temporal dependencies in spatiotemporal data using GNNs. However, the strong interdisciplinary nature of spatiotemporal data has created numerous GNNs variants specifically designed for distinct application domains. Although the techniques are generally applicable across various domains, cross-referencing these methods remains essential yet challenging due to the absence of a comprehensive literature review on GNNs for spatiotemporal data. This article aims to provide a systematic and comprehensive overview of the technologies and applications of GNNs in the spatiotemporal domain. First, the ways of constructing graphs from spatiotemporal data are summarized to help domain experts understand how to generate graphs from various types of spatiotemporal data. Then, a systematic categorization and summary of existing spatiotemporal GNNs are presented to enable domain experts to identify suitable techniques and to support model developers in advancing their research. Moreover, a comprehensive overview of significant applications in the spatiotemporal domain is offered to introduce a broader range of applications to model developers and domain experts, assisting them in exploring potential research topics and enhancing the impact of their work. Finally, open challenges and future directions are discussed.