Recently, deep learning (DL) has achieved great success in biometric recognition. The application of DL has also led to a high demand for biometric data. However, as people attach more importance to privacy protection, biometric data have become increasingly difficult to obtain and access, leading to significant limitations in the development and application of DL-based biometric recognition. Federated learning (FL), a distributed learning technique with privacy protection, provides a potential solution to this problem. Several researchers have attempted to integrate FL into biometric recognition. These studies have shown that the introduction of FL not only solves the conflict between privacy and accessibility of biometric data but also improves the accuracy and generalizability of local recognition systems. Therefore, the combination of FL and biometric recognition techniques has become a new research hotspot. In this survey, we comprehensively review the latest advances regarding the application of FL to biometric recognition, biometric presentation attack detection and the related fields to provide new researchers with a quick and systematic overview of this emerging cross-disciplinary field. This paper also summarizes the future opportunities and challenges of this field. To our knowledge, this is the first survey that systematically organizes and analyses federated biometric recognition and related fields to provide suggestions and references for future research.