Time-series forecasting has long been studied and remains an important research task. In scenarios where multiple time series need to be forecast, approaches that exploit the mutual impact between time series results in more accurate forecasts. This has been demonstrated in various applications, including demand forecasting and traffic forecasting, among others. Hence, this dissertation focuses on graph-based models, which leverage the internode relations to forecast more efficiently and effectively by associating time series with nodes. This dissertation begins by introducing the notion of graph time-series models in a comprehensive survey of related models. The main contributions of this survey are: (1) A novel categorization is proposed to thoroughly analyze over 20 representative graph time-series models from various perspectives, including temporal components, propagation procedures, and graph construction methods, among others. (2) Similarities and differences among models are discussed to provide a fundamental understanding of decisive factors in graph time-series models. Model challenges and future directions are also discussed. Following the survey, this dissertation develops graph time-series models that utilize complex time-series interactions to yield context-aware, real-time, and probabilistic forecasting. The first method, Context Integrated Graph Neural Network (CIGNN), targets resource forecasting with contextual data. Previous solutions either neglect contextual data or only leverage static features, which fail to exploit contextual information. Its main contributions include: (1) Integrating multiple contextual graphs; and (2) Introducing and incorporating temporal, spatial, relational, and contextual dependencies; The second method, Evolving Super Graph Neural Network (ESGNN), targets large-scale time-series datasets through training on super graphs. Most graph time-series models let each node associate with a time series, potentially resulting in a high time cost. Its main contributions include: (1) Generating multiple super graphs to reflect node dynamics at different periods; and (2) Proposing an efficient super graph construction method based on K-Means and LSH; The third method, Probabilistic Hypergraph Recurrent Neural Network (PHRNN), targets datasets under the assumption that nodes interact in a simultaneous broadcasting manner. Previous hypergraph approaches leverage a static weight hypergraph, which fails to capture the interaction dynamics among nodes. Its main contributions include: (1) Learning a probabilistic hypergraph structure from the time series; and (2) Proposing the use of a KNN hypergraph for hypergraph initialization and regularization. The last method, Graph Deep Factors (GraphDF), aims at efficient and effective probabilistic forecasting. Previous probabilistic approaches neglect the interrelations between time series. Its main contributions include: (1) Proposing a framework that consists of a relational global component and a relational local component; (2) Conducting analysis in terms of accuracy, efficiency, scalability, and simulation with opportunistic scheduling. (3) Designing an algorithm for incremental online learning. / Doctor of Philosophy / Time-series forecasting has long been studied due to its usefulness in numerous applications, including demand forecasting, traffic forecasting, and workload forecasting, among others. In scenarios where multiple time series need to be forecast, approaches that exploit the mutual impact between time series results in more accurate forecasts. Hence, this dissertation focuses on a specific area of deep learning: graph time-series models. These models associate time series with a graph structure for more efficient and effective forecasting. This dissertation introduces the notion of graph time series through a comprehensive survey and analyzes representative graph time-series models to help readers gain a fundamental understanding of graph time series. Following the survey, this dissertation develops graph time-series models that utilize complex time-series interactions to yield context-aware, real-time, and probabilistic forecasting. The first method, Context Integrated Graph Neural Network (CIGNN), incorporates multiple contextual graph time series for resource time-series forecasting. The second method, Evolving Super Graph Neural Network (ESGNN), constructs dynamic super graphs for large-scale time-series forecasting. The third method, Probabilistic Hypergraph Recurrent Neural Network (PHRNN), designs a probabilistic hypergraph model that learns the interactions between nodes as distributions in a hypergraph structure. The last method, Graph Deep Factors (GraphDF), targets probabilistic time-series forecasting with a relational global component and a relational local model. These methods collectively covers various data characteristics and model structures, including graphs, super graph, and hypergraphs; a single graph, dual graphs, and multiple graphs; point forecasting and probabilistic forecasting; offline learning and online learning; and both small and large-scale datasets. This dissertation also highlights the similarities and differences between these methods. In the end, future directions in the area of graph time series are also provided.