Digital watermarking is the art of embedding secret messages in multimedia contents in order to protect their intellectual property. While the watermarking of image, audio and video is reaching maturity, the watermarking of 3D virtual objects is still a technology in its infancy. In this thesis, we focus on two main issues. The first one is the perception of the distortions caused by the watermarking process or by attacks on the surface of a 3D model. The second one concerns the development of techniques able to retrieve a watermark without the availability of the original data and after common manipulations and attacks. Since imperceptibility is a strong requirement, assessing the visual perception of the distortions that a 3D model undergoes in the watermarking pipeline is a key issue. In this thesis, we propose an image-based metric that relies on the comparison of 2D views with a Mutual Information criterion. A psychovisual experiment has validated the results of this metric for the most common watermarking attacks. The other issue this thesis deals with is the blind and robust watermarking of 3D shapes. In this context, three different watermarking schemes are proposed. These schemes differ by the classes of 3D watermarking attacks they are able to resist to. The first scheme is based on the extension of spectral decomposition to 3D models. This approach leads to robustness against imperceptible geometric deformations. The weakness of this technique is mainly related to resampling or cropping attacks. The second scheme extends the first to resampling by making use of the automatic multiscale detection of robust umbilical points. The third scheme then addresses the cropping attack by detecting robust prong feature points to locally embed a watermark in the spatial domain.