In recent years, the notion of ``the right to be forgotten" (RTBF) has evolved into a fundamental element of data privacy regulations, affording individuals the ability to request the removal of their personal data from digital records. Consequently, given the extensive adoption of data-intensive machine learning (ML) algorithms and increasing concerns for personal data privacy protection, the concept of machine unlearning (MU) has gained considerable attention. MU empowers an ML model to selectively eliminate sensitive or personally identifiable information it acquired during the training process. Evolving from the foundational principles of MU, federated unlearning (FU) has emerged to confront the challenge of data erasure within the domain of federated learning (FL) settings. This empowers the FL model to unlearn an FL client or identifiable information pertaining to the client while preserving the integrity of the decentralized learning process. Nevertheless, unlike traditional MU, the distinctive attributes of federated learning introduce specific challenges for FU techniques. These challenges lead to the need for tailored design when designing FU algorithms. Therefore, this comprehensive survey delves into the techniques, methodologies, and recent advancements in federated unlearning. It provides an overview of fundamental concepts and principles, evaluates existing federated unlearning algorithms, reviews optimizations tailored to federated learning, engages in discussions regarding practical applications, along with an assessment of their limitations, and outlines promising directions for future research.

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