Reversible data hiding is a technique that allows embedding hidden data in host data, such that the host data consistency is perfectly preserved. The host data are restored to their original form after the extraction process retrieves the hidden data. This is also referred as lossless data hiding. Semi-reversible data hiding implies that the host data are not recovered perfectly but that the recovered data are more similar to the host data than the stego data. Reversible data hiding is considered useful for authentication, metadata recording, tampering detection, covert communication, and quality enhancement, and so forth. The technological requirements are minimal stego signal quality degradation, large payload, and undetectable hidden data concealment. This chapter introduces basic reversible data hiding methods. It then introduces recent progress in reversible audio data hiding techniques in the spectral and time domains. The proposed methods are evaluated using the payload amount, the objective quality degradation of stego signals, and payload data concealment.