In recent years, the growth of the Internet along with multimedia data delivery, have caused the misuse and even alteration of the original digital content. As a security mechanism, digital watermarking has been used to protect digital content, traditionally in copyright protection applications, and more recently digital watermarking has been used in content enhancement applications. Regardless of the application, digital watermarking schemes always cause some level of signal degradation. There are however, certain applications as in the military or medical fields, where loss of information cannot be tolerated during the reconstruction of host signals, therefore conventional watermarking schemes do not satisfy the quality requirements. In order to reconstruct signals without loss of data, reversible watermarking is employed. Recent research in reversible watermarking has focused on either, the improvement of embedding capacity or the reduction of perceptual impact of the schemes, but scarcely exploring the robustness of reversible schemes. In this survey, we provide a deep review of reversible watermarking schemes and propose a new classification outline based on the robustness point of view. Finally, some future directions for reversible watermarking research are presented and open problems in robust reversible watermarking are outlined. INDEX TERMS Digital watermarking, multimedia content, reversible watermarking, robustness.