The widespread adoption of smart technologies and digital services has intensified the demand for reliable and secure identity authentication systems. Biometric credentials, offering significant advantages over traditional methods, have emerged as a preferred solution. However, preserving the privacy of biometric data remains a critical challenge. This paper presents a comprehensive study of privacy-preserving techniques and potential risks associated with biometric systems. A novel taxonomy and structured framework are introduced to classify existing research in this domain. The study evaluates state-of-the-art approaches across a wide range of biometric modalities, including facial recognition, fingerprint analysis, eye-based identification, Electroencephalogram (EEG), Electrocardiogram (ECG), voice recognition, and hand geometry, highlighting their respective benefits, limitations, and application areas. Additionally, the paper examines the balance between privacy, security, and recognition performance, addressing current challenges and proposing future research directions. This work serves as a valuable resource for researchers and industry professionals, supporting the development of privacy-centric and secure biometric authentication technologies in an evolving digital landscape.