This paper provides a comprehensive review of open-world machine learning, focusing on unknown rejection, novel class discovery, and class-incremental learning. It discusses the challenges, principles, and limitations of current methodologies and highlights potential future research directions. The authors aim to help researchers build more powerful AI systems and promote the development of artificial general intelligence. The paper begins by introducing the concept of open-world machine learning, emphasizing the need for models to handle unknown inputs and discover new classes in dynamic and uncertain environments. It then outlines the general life cycle of an open-world learning paradigm, which includes unknown rejection, novel class discovery, and class-incremental learning. The background section delves into the problem formulation and notations, detailing the key tasks and their objectives. It also discusses canonical applications such as autonomous driving, medical diagnosis, and AI chatbots, highlighting how open-world learning can enhance these systems' adaptability and robustness. The paper reviews recent advances in unknown rejection techniques, including out-of-distribution (OOD) detection and open-set recognition (OSR). It explores the challenges and methods for improving OOD detection, such as post-hoc inference methods, training-stage methods, and outlier-aided methods. The section on novel class discovery covers multi-stage and one-stage methods, emphasizing the importance of semantic similarity and the estimation of the number of novel classes. Finally, the paper discusses class-incremental learning, addressing the challenges of catastrophic forgetting and presenting various techniques like regularization-based methods, exemplar replay, feature replay, and prompt tuning. The authors conclude by emphasizing the need for further research to overcome existing limitations and achieve more advanced open-world machine learning systems.This paper provides a comprehensive review of open-world machine learning, focusing on unknown rejection, novel class discovery, and class-incremental learning. It discusses the challenges, principles, and limitations of current methodologies and highlights potential future research directions. The authors aim to help researchers build more powerful AI systems and promote the development of artificial general intelligence. The paper begins by introducing the concept of open-world machine learning, emphasizing the need for models to handle unknown inputs and discover new classes in dynamic and uncertain environments. It then outlines the general life cycle of an open-world learning paradigm, which includes unknown rejection, novel class discovery, and class-incremental learning. The background section delves into the problem formulation and notations, detailing the key tasks and their objectives. It also discusses canonical applications such as autonomous driving, medical diagnosis, and AI chatbots, highlighting how open-world learning can enhance these systems' adaptability and robustness. The paper reviews recent advances in unknown rejection techniques, including out-of-distribution (OOD) detection and open-set recognition (OSR). It explores the challenges and methods for improving OOD detection, such as post-hoc inference methods, training-stage methods, and outlier-aided methods. The section on novel class discovery covers multi-stage and one-stage methods, emphasizing the importance of semantic similarity and the estimation of the number of novel classes. Finally, the paper discusses class-incremental learning, addressing the challenges of catastrophic forgetting and presenting various techniques like regularization-based methods, exemplar replay, feature replay, and prompt tuning. The authors conclude by emphasizing the need for further research to overcome existing limitations and achieve more advanced open-world machine learning systems.