In recent years, the Right to Be Forgotten (RTBF) has emerged as a critical issue in promoting digital trust and AI safety, highlighting the necessity of effectively removing identifiable information from trained machine learning models. This necessity has stimulated the development of Machine Unlearning (MU), enabling ML models to selectively remove specific data contributions without retraining from scratch. Building upon MU, Federated Unlearning (FU) has been developed to address data deletion challenges inherent in Federated Learning (FL) scenarios, granting federated models the capability to selectively remove the contributions of specific clients or identifiable client-related data. However, the unique characteristics of federated learning pose additional challenges that cannot be fully addressed by existing centralized unlearning approaches. In this survey, we first provide a concise overview of the FU framework, followed by a detailed introduction to the concepts and definitions related to MU and FU. We then summarize the key challenges currently faced in federated unlearning research. Furthermore, we systematically classify existing federated unlearning algorithms according to their specific tuning objectives. Finally, we outline several promising research directions for future investigations in the field of federated unlearning.