Data hiding or information hiding is a prominent class of information security that aims at reliably conveying secret data embedded in a cover object over a covert channel. Digital media such as audio, image, video, and three-dimensional (3D) media can act as cover objects to carry such secret data. Digital media security has acquired tremendous significance in recent years and will be even more important with the development and delivery of new digital media over digital communication networks. In particular, least significant bit (LSB) data hiding is easy to implement and to combine with other hiding techniques, offers high embedding capacity for data, can resist steganalysis and several types of attacks, and is well suited for real-time applications. This article provides a comprehensive survey on LSB data hiding in digital media. The fundamental concepts and terminologies used in data hiding are reviewed along with a general data hiding model. The five attributes of data hiding, i.e., capacity, imperceptibility, robustness, detectability, and security, and the related performance metrics used in this survey to compare the characteristics of the different LSB data hiding methods are discussed. Given the classification of data hiding methods with respect to audio, image, video, and 3D media, a comprehensive survey of LSB data hiding for each of these four digital media is provided. In particular, landmark studies, state-of-the-art approaches, and applications of LSB data hiding are described for each of the four digital media. Their performance is compared with respect to the data hiding attributes which illustrates benefits and drawbacks of the reviewed LSB data hiding methods. The article concludes with summarizing main findings and suggesting directions for future research. This survey will be helpful for researchers and practitioners to keep abreast about the potential of LSB data hiding in digital media and to develop novel applications based on suitable performance trade-offs between data hiding attributes.