This paper reviews the challenges of small data in prognostics and health management (PHM), focusing on fundamental concepts, current research, and future directions. PHM is crucial for improving equipment reliability and reducing maintenance costs, but real-world scenarios pose small-data challenges due to limited data collection and complex working conditions. The paper explores data augmentation, transfer learning, and few-shot learning techniques to address these challenges. It summarizes benchmark datasets and experimental paradigms to evaluate diverse methodologies under small data conditions. The paper highlights promising directions for future research. PHM involves four key dimensions: anomaly detection (AD), fault diagnosis (FD), remaining useful life (RUL) prediction, and maintenance execution (ME). Techniques for PHM include physics model-based, data-driven, and hybrid methods. Deep learning (DL) has gained significant interest due to its advantages in automatic feature extraction and pattern recognition. Small data in PHM refers to datasets with limited quantity or quality of samples, often due to limited fault categories or sample size. It is characterized by incomplete data, imbalanced distribution, and poor model generalization. The paper analyzes the causes of small data problems, including heavy investment, data accessibility restrictions, complex working conditions, and multi-factor coupling. It discusses the impacts of small data on PHM tasks, including data incompleteness and imbalanced data distribution. The paper provides an overview of approaches to small data challenges in PHM, including data augmentation (DA), transfer learning (TL), and few-shot learning (FSL). DA methods include transform-based, sampling-based, and deep generative models-based approaches. TL methods involve instance-based, feature-based, and parameter-based approaches. FSL methods focus on learning models that can be quickly adapted to tasks with few examples. The paper concludes that small data challenges in PHM require further research to develop effective solutions. It highlights the importance of addressing these challenges to improve the efficiency and robustness of AI models in industrial applications. The paper provides a comprehensive review of current research and identifies promising directions for future work.This paper reviews the challenges of small data in prognostics and health management (PHM), focusing on fundamental concepts, current research, and future directions. PHM is crucial for improving equipment reliability and reducing maintenance costs, but real-world scenarios pose small-data challenges due to limited data collection and complex working conditions. The paper explores data augmentation, transfer learning, and few-shot learning techniques to address these challenges. It summarizes benchmark datasets and experimental paradigms to evaluate diverse methodologies under small data conditions. The paper highlights promising directions for future research. PHM involves four key dimensions: anomaly detection (AD), fault diagnosis (FD), remaining useful life (RUL) prediction, and maintenance execution (ME). Techniques for PHM include physics model-based, data-driven, and hybrid methods. Deep learning (DL) has gained significant interest due to its advantages in automatic feature extraction and pattern recognition. Small data in PHM refers to datasets with limited quantity or quality of samples, often due to limited fault categories or sample size. It is characterized by incomplete data, imbalanced distribution, and poor model generalization. The paper analyzes the causes of small data problems, including heavy investment, data accessibility restrictions, complex working conditions, and multi-factor coupling. It discusses the impacts of small data on PHM tasks, including data incompleteness and imbalanced data distribution. The paper provides an overview of approaches to small data challenges in PHM, including data augmentation (DA), transfer learning (TL), and few-shot learning (FSL). DA methods include transform-based, sampling-based, and deep generative models-based approaches. TL methods involve instance-based, feature-based, and parameter-based approaches. FSL methods focus on learning models that can be quickly adapted to tasks with few examples. The paper concludes that small data challenges in PHM require further research to develop effective solutions. It highlights the importance of addressing these challenges to improve the efficiency and robustness of AI models in industrial applications. The paper provides a comprehensive review of current research and identifies promising directions for future work.