This book chapter explores the challenges and insights of continual learning, a process where artificial neural networks incrementally learn from non-stationary data streams. Unlike humans, who can retain and build upon previous knowledge, neural networks often suffer from catastrophic forgetting, where they rapidly lose previously learned information when learning new tasks. This phenomenon is a major obstacle in deep learning, as it limits the ability of neural networks to adapt to changing environments. The chapter discusses various approaches to mitigate catastrophic forgetting, including replay, parameter regularization, functional regularization, optimization-based methods, context-dependent processing, and template-based classification. These methods aim to improve the ability of neural networks to retain and build upon previous knowledge while learning new tasks. The chapter also highlights the importance of task-based versus task-free continual learning, and the distinction between task-incremental, domain-incremental, and class-incremental learning scenarios. Evaluation of continual learning methods involves assessing performance, diagnostic analysis, and resource efficiency. The chapter emphasizes the need for methods that can adapt to new situations, exploit task similarity, be task-agnostic, tolerate noise, and operate efficiently in terms of computational and memory resources. It also discusses the potential applications of continual learning in real-world scenarios, such as edge computing and error correction in deep learning models. The chapter concludes by noting that continual learning remains a significant challenge in deep learning, with ongoing research aimed at developing more effective methods that can overcome the limitations of catastrophic forgetting and improve the efficiency and adaptability of neural networks.This book chapter explores the challenges and insights of continual learning, a process where artificial neural networks incrementally learn from non-stationary data streams. Unlike humans, who can retain and build upon previous knowledge, neural networks often suffer from catastrophic forgetting, where they rapidly lose previously learned information when learning new tasks. This phenomenon is a major obstacle in deep learning, as it limits the ability of neural networks to adapt to changing environments. The chapter discusses various approaches to mitigate catastrophic forgetting, including replay, parameter regularization, functional regularization, optimization-based methods, context-dependent processing, and template-based classification. These methods aim to improve the ability of neural networks to retain and build upon previous knowledge while learning new tasks. The chapter also highlights the importance of task-based versus task-free continual learning, and the distinction between task-incremental, domain-incremental, and class-incremental learning scenarios. Evaluation of continual learning methods involves assessing performance, diagnostic analysis, and resource efficiency. The chapter emphasizes the need for methods that can adapt to new situations, exploit task similarity, be task-agnostic, tolerate noise, and operate efficiently in terms of computational and memory resources. It also discusses the potential applications of continual learning in real-world scenarios, such as edge computing and error correction in deep learning models. The chapter concludes by noting that continual learning remains a significant challenge in deep learning, with ongoing research aimed at developing more effective methods that can overcome the limitations of catastrophic forgetting and improve the efficiency and adaptability of neural networks.