Spatial-temporal forecasting and imputation are important for real-world dynamic systems such as intelligent transportation, urban planning, and public health. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less effective for zero-shot and few-shot learning. While large language models (LLMs) have exhibited strong pattern recognition and reasoning abilities across various tasks, including few-shot and zero-shot learning, their development in understanding spatial-temporal data has been constrained by insufficient modeling of complex correlations such as the temporal correlations, spatial connectivity, non-pairwise and high-order spatial-temporal correlations within data. In this paper, we propose STD-LLM for understanding both spatial and temporal properties of \underline{S}patial-\underline{T}emporal \underline{D}ata with \underline{LLM}s, which is capable of implementing both spatial-temporal forecasting and imputation tasks. STD-LLM understands spatial-temporal correlations via explicitly designed spatial and temporal tokenizers as well as virtual nodes. Topology-aware node embeddings are designed for LLMs to comprehend and exploit the topology structure of data. Additionally, to capture the non-pairwise and higher-order correlations, we design a hypergraph learning module for LLMs, which can enhance the overall performance and improve efficiency. Extensive experiments demonstrate that STD-LLM exhibits strong performance and generalization capabilities across the forecasting and imputation tasks on various datasets. Moreover, STD-LLM achieves promising results on both few-shot and zero-shot learning tasks.

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