In recent years, large models have made breakthroughs in natural language processing and computer vision by virtue of their powerful sequence modeling capability, excellent representation learning potential, and flexible pre-training–fine-tuning paradigm, which also bring new development opportunities for time-series and spatio-temporal data intelligent analysis and are expected to revolutionize the analysis paradigm. This paper provides a systematic review of research progress on large models for time series and spatio-temporal data analysis, focusing on two major directions: empowering large language models and building dedicated foundation models. The former leverages prompt engineering, tokenization, and parameter-efficient fine-tuning to adapt large models to time series and spatio-temporal tasks, while the latter employs large-scale cross-domain pre-training to establish unified dynamic representations. The path of empowering large language models offers advantages such as low development costs and flexible zero-shot/few-shot transfer learning, while specialized foundational models demonstrate superior cross-domain generalization capabilities. At the same time, both approaches still face challenges including insufficient interpretability and difficulties in multimodal semantic alignment. Future research urgently requires breakthroughs in enhancing interpretability, advancing multimodal joint modeling, and innovating model architectures.