Three-dimensional computerized characterization of biomedical solid textures is key to large-scale and high-throughput screening of imaging data. Such data increasingly become available in the clinical and research environments with an ever increasing spatial resolution. In this text we exhaustively analyze the state-of-the-art in 3-D biomedical texture analysis to identify the specific needs of the application domains and extract promising trends in image processing algorithms. The geometrical properties of biomedical textures are studied both in their natural space and on digitized lattices. It is found that most of the tissue types have strong multi-scale directional properties, that are well captured by imaging protocols with high resolutions and spherical spatial transfer functions. The information modeled by the various image processing techniques is analyzed and visualized by displaying their 3-D texture primitives. We demonstrate that non-convolutional approaches are expected to provide best results when the size of structures are inferior to five voxels. For larger structures, it is shown that only multi-scale directional convolutional approaches that are non-separable allow for an unbiased modeling of 3-D biomedical textures. With the increase of high-resolution isotropic imaging protocols in clinical routine and research, these models are expected to best leverage the wealth of 3-D biomedical texture analysis in the future. Future research directions and opportunities are proposed to efficiently model personalized image-based phenotypes of normal biomedical tissue and its alterations. The integration of the clinical and genomic context is expected to better explain the intra class variation of healthy biomedical textures. Using texture synthesis, this provides the exciting opportunity to simulate and visualize texture atlases of normal ageing process and disease progression for enhanced treatment planning and clinical care management.