Open-world machine learning (OWL) is a paradigm that enables models to handle dynamic, uncertain environments by continuously learning from new data and adapting to novel classes. Unlike closed-world assumptions, which assume the environment is static and known, OWL allows models to reject unknowns, discover new classes, and incrementally learn them. This paper provides a comprehensive review of OWL, focusing on three key tasks: unknown rejection, novel class discovery, and class-incremental learning. It discusses the challenges, principles, and limitations of current methodologies, as well as potential future research directions. The paper begins with an introduction to OWL, highlighting its importance in real-world applications such as autonomous driving, medical diagnosis, and AI chatbots. It then presents a problem formulation and notations for OWL, followed by a discussion of canonical use cases. The paper then delves into the challenges of OWL, including the need for models to recognize unknowns, discover new classes, and learn incrementally without catastrophic forgetting. The paper then provides an in-depth analysis of unknown rejection, discussing various methods such as out-of-distribution (OOD) detection and open-set recognition (OSR). It explores the key challenges in unknown rejection, including the difficulty of distinguishing between OOD and in-distribution samples, and presents various techniques for improving OOD detection, such as post-hoc inference methods, training-stage methods, and outlier-aided methods. Next, the paper discusses novel class discovery, which involves automatically discovering new categories from unlabeled data. It presents different methods for novel class discovery, including multi-stage and one-stage approaches, and discusses the challenges of estimating the number of novel classes. Finally, the paper addresses class-incremental learning, which involves continuously extending the multi-class classifier to learn new classes without forgetting previously learned knowledge. It discusses the key challenges of class-incremental learning, including catastrophic forgetting, and presents various methods such as regularization-based, exemplar replay, feature replay, and prompt-based approaches. Overall, the paper provides a comprehensive overview of open-world machine learning, highlighting its importance in real-world applications and the challenges and opportunities for future research.Open-world machine learning (OWL) is a paradigm that enables models to handle dynamic, uncertain environments by continuously learning from new data and adapting to novel classes. Unlike closed-world assumptions, which assume the environment is static and known, OWL allows models to reject unknowns, discover new classes, and incrementally learn them. This paper provides a comprehensive review of OWL, focusing on three key tasks: unknown rejection, novel class discovery, and class-incremental learning. It discusses the challenges, principles, and limitations of current methodologies, as well as potential future research directions. The paper begins with an introduction to OWL, highlighting its importance in real-world applications such as autonomous driving, medical diagnosis, and AI chatbots. It then presents a problem formulation and notations for OWL, followed by a discussion of canonical use cases. The paper then delves into the challenges of OWL, including the need for models to recognize unknowns, discover new classes, and learn incrementally without catastrophic forgetting. The paper then provides an in-depth analysis of unknown rejection, discussing various methods such as out-of-distribution (OOD) detection and open-set recognition (OSR). It explores the key challenges in unknown rejection, including the difficulty of distinguishing between OOD and in-distribution samples, and presents various techniques for improving OOD detection, such as post-hoc inference methods, training-stage methods, and outlier-aided methods. Next, the paper discusses novel class discovery, which involves automatically discovering new categories from unlabeled data. It presents different methods for novel class discovery, including multi-stage and one-stage approaches, and discusses the challenges of estimating the number of novel classes. Finally, the paper addresses class-incremental learning, which involves continuously extending the multi-class classifier to learn new classes without forgetting previously learned knowledge. It discusses the key challenges of class-incremental learning, including catastrophic forgetting, and presents various methods such as regularization-based, exemplar replay, feature replay, and prompt-based approaches. Overall, the paper provides a comprehensive overview of open-world machine learning, highlighting its importance in real-world applications and the challenges and opportunities for future research.