Digital watermarking for authentication and copyright protection is one of the interesting areas of research in information security. This technique is no more limited to the images but also applied to the audio, video, softwares and databases. However, the limitation of digital watermarking is that it introduces small distortions in the original cover contents, thus causing slight degradation. These distortions are undesirable in some sensitive applications data like medical, military and law-enforcement etc, where imperceptibility is also desired. However, there are certain applications in which this requirement is just opposite. For example, in medical images, the original image contents must be hidden from the naked eye to ensure the privacy. The problem is formulated into two parts. Firstly, to enhance the security of medical images by hiding the contents of image along with the recovery and fragility. Secondly, to optimize the three conflicting parameters of digital watermarking namely, capacity, imperceptibility and robustness so that we could find an appropriate way to embed the watermark information in the image while satisfying the said parameters.In the first part, our main thrust is that image contents should not be visible to the naked eye. Moreover, the watermarked image should be recoverable along with the watermark on the receiving end. Lastly any tampering in the image should be detectable. In this regard, we have proposed residue number system (RNS) along with the chaotic key for the reversible watermarking of medical images by presenting five different schemes. In the first two schemes, watermark information and original image both are fragile, so that any tampering in the image contents can be easily indicated. In the rest of the schemes, image is kept fragile, while the watermark information is made robust so that it can withstand some reasonable amount of modifications. The second part is concerned with general images carrying hidden information. Our main focus is to optimize the three parameters of digital watermarking, namely capacity, imperceptibility and robustness. In this regard, we have proposed a fuzzy rule base system (FRBS) along with human visual system (HVS) in three different schemes. In first two schemes, FRBS for optimizing capacity or imperceptibility is proposed while keeping the other fixed. It is achieved by finding the HVS features of the image and then tradeoff is made between the imperceptibility and viii capacity using FRBS. In the third scheme, we have jointly optimized the three parameters using FRBS and HVS. In summary, efficient watermarking schemes are developed which can protect the medical images from the naked eye along with the reversibility and fragility. The proposed schemes for the second part can also either optimize the two parameters or jointly optimize the three parameters. The proposed schemes are compared with the well known schemes of digital watermarking in the literature.