This paper provides a comprehensive survey of model compression techniques in biometrics applications, focusing on quantization, knowledge distillation, and pruning. The authors aim to systematize the current literature and critically analyze the comparative value of these techniques, highlighting their advantages and disadvantages. They also discuss the link between model bias and model compression, emphasizing the need for future research to address model fairness. The paper begins by defining the three main groups of compression techniques and then explores the current state of the art in each technique, including their mathematical foundations and practical applications. It reviews several studies that have applied these techniques to biometric systems, such as face recognition, and discusses the impact of different factors like quantization functions, strategies, granularity, and global algorithms. The paper also delves into the details of knowledge distillation, including supervised learning, response-based, feature-based, and relation-based approaches, and their implementation in biometric models. Finally, it examines pruning techniques, their sparsity levels, granularities, criteria, and strategies, and their impact on model performance and deployment. The authors conclude with a critical analysis of the existing literature and suggest future research directions to improve the effectiveness and fairness of model compression techniques in biometric applications.This paper provides a comprehensive survey of model compression techniques in biometrics applications, focusing on quantization, knowledge distillation, and pruning. The authors aim to systematize the current literature and critically analyze the comparative value of these techniques, highlighting their advantages and disadvantages. They also discuss the link between model bias and model compression, emphasizing the need for future research to address model fairness. The paper begins by defining the three main groups of compression techniques and then explores the current state of the art in each technique, including their mathematical foundations and practical applications. It reviews several studies that have applied these techniques to biometric systems, such as face recognition, and discusses the impact of different factors like quantization functions, strategies, granularity, and global algorithms. The paper also delves into the details of knowledge distillation, including supervised learning, response-based, feature-based, and relation-based approaches, and their implementation in biometric models. Finally, it examines pruning techniques, their sparsity levels, granularities, criteria, and strategies, and their impact on model performance and deployment. The authors conclude with a critical analysis of the existing literature and suggest future research directions to improve the effectiveness and fairness of model compression techniques in biometric applications.