With the development of sensing technology, lots of spatio-temporal data springs up in different fields. The spatio-temporal graph is a major type of spatio-temporal data with complex structure, spatio-temporal features, and relationships. How to mine key patterns from complex spatio-temporal graph data for various downstream tasks has become the main problem of complex spatio-temporal data mining tasks. Currently, the increasingly mature temporal graph neural networks provide powerful tools for the development of this research field. In addition, the emerging spatio-temporal large models provide a new research perspective based on the existing spatio-temporal graph neural network methods. However, most existing reviews in this field have relatively rough classification frameworks for methods, lack comprehensive and in-depth introduction to complex data types (e.g., dynamic heterogeneous graphs and dynamic hypergraphs), and do not provide a detailed summary of the latest research progress related to spatio-temporal graph large models. Therefore, in this study, the complex spatio-temporal data mining methods based on graph neural networks are divided into spatio-temporal fusion architecture and spatio-temporal large models to introduce them from traditional and emerging perspectives. According to specific complex data types, spatio-temporal fusion architecture is divided into dynamic graphs, dynamic heterogeneous graphs, and dynamic hypergraphs. Moreover, the spatio-temporal large models are divided into time series and graphs according to temporal and spatial dimensions. The latest research related to spatio-temporal graphs is listed in graph-based large models. The core details of multiple key algorithms are introduced, and the pros and cons of different methods are compared. Finally, the application fields and commonly used datasets of complex spatio-temporal data mining methods based on graph neural networks are listed, and possible future research directions are outlined.