Class-incremental learning (CIL) aims to enable models to maintain discriminative ability on previously learned classes while incrementally acquiring new ones, a process in which catastrophic forgetting often occurs. This paper provides a comprehensive survey and analysis of class-incremental learning and its development trends. We clarified the definition of CIL and distinguished it from other incremental learning settings. Mainstream approaches were categorized and summarized from five perspectives: memory replay, parameter and optimization constraints, model prediction calibration, model architecture design, and transfer of pre-trained models. In addition, the commonly used evaluation metrics and datasets of CIL were reviewed, and its applications in typical vision tasks such as image generation, object detection, and semantic segmentation, as well as in emerging areas including video understanding and 3D vision were summarized. Finally, the future research directions of CIL were prospected.