Technological advances in the fields of telecommunication, computer graphics and hardware design during the two last decades have contributed to the emergence of three-dimensional (3D) data in many industrial domains (scientific visualization, digital entertainment, mechanical engineering, cultural heritage). At the same time the range of terminals capable of visualizing 3D data is now expanding to mobile devices such as tablets and smartphones; besides, the visualization of 3D content through the Web is now possible. This heterogeneity of uses and terminals induces a need for effective tools to ensure easy access to 3D databases, as well as visualization and secure transmission of this 3D content. This Habilitation, which covers the period of my professional activity since September 2006, summarizes the research I have conducted regarding this scenario of acces, visualization and secure transmission of 3D meshes. Our contributions concern three distinct topics of research: compression (reduction of the size of data especially by considering multi-resolution methods), watermarking (protection of the intellectual property of 3D content by inserting a hidden mark) and indexing (proposition of 3D shape descriptors and efficient retrieval algorithms). Our work on these three topics have been conducted by considering two strong transverse aspects: (1) an upstream analysis step, including contributions to 3D segmentation and above (2) a continuous link with the notions of quality evaluation and visual perception. We have studied the perceptual mechanisms involved in computer graphics through multiple subjective experiments and we have introduced metrics to predict the visual quality. This Habilitation concludes with a description of my research project that focuses on the interactive remote visualization of 3D data on two emerging multimedia environments: Web platforms and mobile devices.