In recent years, the notion of ``the right to be forgotten" (RTBF) has become a crucial aspect of data privacy for digital trust and AI safety, requiring the provision of mechanisms that support the removal of personal data of individuals upon their requests. Consequently, machine unlearning (MU) has gained considerable attention which allows an ML model to selectively eliminate identifiable information. Evolving from MU, federated unlearning (FU) has emerged to confront the challenge of data erasure within federated learning (FL) settings, which empowers the FL model to unlearn an FL client or identifiable information pertaining to the client. Nevertheless, the distinctive attributes of federated learning introduce specific challenges for FU techniques. These challenges necessitate a tailored design when developing FU algorithms. While various concepts and numerous federated unlearning schemes exist in this field, the unified workflow and tailored design of FU are not yet well understood. Therefore, this comprehensive survey delves into the techniques and methodologies in FU providing an overview of fundamental concepts and principles, evaluating existing federated unlearning algorithms, and reviewing optimizations tailored to federated learning. Additionally, it discusses practical applications and assesses their limitations. Finally, it outlines promising directions for future research.