The ease with which digital data can be duplicated and distributed over the media and the Internet has raised many concerns about copyright infringement. In many situations, multimedia data (e.g., images, music, movies, etc) are illegally circulated, thus violating intellectual property rights. In an attempt to overcome this problem, watermarking has been suggested in the literature as the most effective means for copyright protection and authentication. Watermarking is the procedure whereby information (pertaining to owner and/or copyright) is embedded into host data, such that it is: (i) hidden, i.e., not perceptually visible; and (ii) recoverable, even after a (possibly malicious) degradation of the protected work. In this thesis, we prove some theoretical results that establish the fundamental limits of a general class of watermarking schemes.