Micro-expressions can reveal genuine emotions that individuals attempt to conceal and therefore have significant application value in areas such as lie detection, healthcare, and fine-grained emotion recognition. Unlike macro-expressions, micro-expressions are brief and subtle facial movements. In addition, the construction of micro-expression datasets involves high costs and considerable effort, which results in limited data availability and makes it difficult for models to capture subtle and transient facial changes. Micro-expression analysis mainly consists of two important research branches: micro-expression recognition and micro-expression detection. Currently, deep learning-based methods dominate research in this field. Accordingly, this study comprehensively reviews representative works and recent advances in deep learning-based micro-expression recognition and micro-expression detection. Firstly, the study provides a systematic summary of commonly used open-source micro-expression datasets. Secondly, it separately introduces representative research on micro-expression recognition (MER) and micro-expression detection (MED), classifies and organizes these methods, and discusses their respective advantages and limitations. Furthermore, it presents commonly used evaluation protocols and metrics for micro-expression analysis and integrates discussions on the performance of various methods. Finally, it summarizes the overall development of micro-expression analysis and offers insights into future research directions.