Three-dimensional (3-D) meshes are commonly used to represent virtual surfaces and volumes. Over the past decade, 3-D meshes have emerged in industrial, medical, and entertainment applications, being of large practical significance for 3-D mesh steganography and steganalysis. In this article, we provide a systematic survey of the literature on 3-D mesh steganography and steganalysis. Compared with an earlier survey [1], we propose a new taxonomy of steganographic algorithms with four categories: 1) two-state domain, 2) LSB domain, 3) permutation domain, and 4) transform domain. Regarding steganalysis algorithms, we divide them into two categories: 1) universal steganalysis and 2) specific steganalysis. For each category, the history of technical developments and the current technological level are introduced and discussed. Finally, we highlight some promising future research directions and challenges in improving the performance of 3-D mesh steganography and steganalysis.