Three-dimensional (3-D) meshes have been used more and more in industrial, medical and entertainment applications during the last decade. Many researchers, from both the academic and the industrial sectors, have become aware of their intellectual property protection and authentication problems arising with their increasing use. This paper gives a comprehensive survey on 3-D mesh watermarking, which is considered an effective solution to the above two emerging problems. Our survey covers an introduction to the relevant state of the art, an attack-centric investigation, and a list of existing problems and potential solutions. First, the particular difficulties encountered while applying watermarking on 3-D meshes are discussed. Then we give a presentation and an analysis of the existing algorithms by distinguishing them between fragile techniques and robust techniques. Since attacks play an important role in the design of 3-D mesh watermarking algorithms, we also provide an attack-centric viewpoint of this state of the art. Finally, some future working directions are pointed out especially on the ways of devising robust and blind algorithms and on some new probably promising watermarking feature spaces.