The development of information technology has led to a significant increase in the share of multimedia traffic in data networks. This has necessitated to solve the following information security tasks in relation to multimedia data: protection against leakage of confidential information, as well as identifying the source of the leak; ensuring the impossibility of unauthorized changes; copyright protection for digital objects. To solve such kind of problems, methods of steganography and watermarking are designed that implement embedding in digital objects hidden information sequences for various purposes. In this paper, an overview of promising research in the specified area is provided. First of all, we provide basic information about this field of research and consider the main applications of its methods. Next, we review works demonstrating current trends in the development of methods and algorithms for data hiding in digital images. This review is not exhaustive; it focuses on contemporary works illustrating current research directions in the field of information embedding in digital images. This is the main feature of review, which distinguishes it from previously published reviews. The paper concludes with an analysis of identified problems in the field of digital steganography and digital watermarking.