Temporal data, including time series and spatio-temporal data, are pervasive in real-world applications. Generated in massive volumes by physical and virtual sensors, they record dynamic system behaviors and enable a wide range of downstream tasks. Effectively analyzing such data is crucial to unlocking their rich information content. Recent advances in large language models and other foundation models have accelerated their use in time series and spatio-temporal data mining. These approaches not only improve pattern recognition and reasoning across diverse domains but also support progress toward artificial general intelligence that can understand and process temporal data. In this survey, we present a comprehensive, up-to-date review of large models tailored or adapted for time series and spatio-temporal data along four dimensions: data types, model categories, model scopes, and application areas/tasks. We organize existing work into two main groups: large models for time series analysis (LM4TS) and for spatio-temporal data mining (LM4STD), and further distinguish general-purpose from domain-specific models. We also curate related resources, including datasets, model implementations, and tools, organized by major application areas. Overall, this survey consolidates recent advances and highlights foundations, applications, resources, and open research opportunities in large model-centric temporal data analysis.