In recent years, spatio-temporal graph neural networks (GNNs) have attracted considerable interest in the field of time series analysis, due to their ability to capture, at once, dependencies among variables and across time points. The objective of this systematic literature review is hence to provide a comprehensive overview of the various modeling approaches and application domains of GNNs for time series classification and forecasting. A database search was conducted, and 366 papers were selected for a detailed examination of the current state-of-the-art in the field. This examination is intended to offer to the reader a comprehensive review of proposed models, links to related source code, available datasets, benchmark models, and fitting results. All this information is hoped to assist researchers in their studies. To the best of our knowledge, this is the first and broadest systematic literature review presenting a detailed comparison of results from current spatio-temporal GNN models applied to different domains. In its final part, this review discusses current limitations and challenges in the application of spatio-temporal GNNs, such as comparability, reproducibility, explainability, poor information capacity, and scalability. This paper is complemented by a GitHub repository at https://github.com/FlaGer99/SLR-Spatio-Temporal-GNN.git providing additional interactive tools to further explore the presented findings.