This paper firstly gives a brief overview of information embedding in deoxyribonucleic acid (DNA) sequences and its applications. DNA data embedding can be considered as a particular case of communications with or without side information, depending on the use of coding or noncoding DNA sequences, respectively. Although several DNA data embedding methods have been proposed over the last decade, it is still an open question to determine the maximum amount of information that can theoretically be embedded —that is, its Shannon capacity. This is the main question tackled in this paper.