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Face anti-spoofing (FAS), as an important means to protect face recognition models, can ensure that the system remains secure and reliable in the face of various presentation attacks. The current deep learning-based face anti-spoofing model has satisfactory results when the test data and training data obey the same distribution, but the accuracy of the model decreases considerably when the trained model infers in the scene outside the domain, such as cross-domain transfer and out-of-distribution scenarios. The problems that silent face anti-spoofing models will encounter in real scenarios, i.e., the models encounter unknown environments and unknown attack methods, are mainly described. The corresponding solutions are classified into four categories: methods based on domain adaptation, methods based on domain generalization, methods based on zero shot or few shot learning, and methods based on anomaly detection. Each solution and its deep learning model methods are summarized and compared. The mechanism, network structure, advantages, limitations and application scenarios of some major methods are summarized. After that, common public datasets, evaluation metrics, measurement protocols commonly used for face anti-spoofing in out of domain scenarios and test results of state-of-the-art methods under some protocols are introduced. Finally, the difficulties and challenges of face anti-spoofing in practical applications are discussed, and future research directions are summarized.