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Recent advances in single-cell sequencing technologies have enabled the measurement of single-cell characteristics over multiple time points. However, the integration and analysis of these dynamic single-cell data face many challenges and raise new demands for computational methodologies. In this review, we first elaborate these challenges in the context of experimental limitations, data features, and biological discoveries. Then, we provide an overview of the algorithmic advancements across four key tasks: inferring single-cell dynamics, dissecting dynamic mechanisms, predicting future cell fates, and integrating lineage tracing information to characterize cell dynamics. 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