Steganography is a popular research direction in the field of information security. Due to the widespread use of video media, video steganography has received much attention from the research community. Among video steganography, motion vector (MV)-based video steganography has become one of the critical concerns of researchers due to its large embedding capacity and high visual quality. In this article, we focus on the research of MV-based video steganography. Firstly, the basic principles and evaluation criteria for MV-based steganography are discussed. Secondly, according to the different technical characteristics, the MV-based steganography is divided into three categories: the traditional MV domain steganography, the code-based MV domain steganography, and the adaptive MV domain steganography based on the framework of minimizing embedding distortion. The advantages and possible improvement directions of the above representative methods are illustrated. And then, the MV-based video steganalysis is outlined according to different perspectives of feature extraction, which is conducive to the design of better steganography algorithms. Finally, five future research directions are presented, such as designing distortion functions based on multiple factors, embedding methods based on new video coding standards, deep learning-based MV steganography, multidomain embedding strategies, and moving the MV-based steganography from the laboratory into the real world.