In this talk, an overview will be given about a new research initiative on bone micromechanics that is currently being pursued in the Laboratory for Micro-, Nano-, and Bio-Mechanics of Materials at SMU. Biological tissue materials such as bones and muscles are commonly hierarchal complex 3D systems and their properties and functions are intrinsically linked to their underlying morphological and compositional details over a wide range of spatial scales. To improve the understanding of such linkages, one can carry out large scale numerical simulation of materials using ever increasing computational resources. However, one often needs to access the detailed microstructural information that fully accounts for the three-dimensional aspects of material microstructure in order to achieve consistent and reliable simulation results. A combined computational and experimental approach is being used in our lab to develop advanced material models of bones that can be used to predict their basic mechanical properties as well as their complex deformation and fracture behavior. Various challenges in computational materials science, solid mechanics, and mathematics in the research will be pointed out. Relevance of the research to biomedical applications such as improved diagnosis and treatment of osteoporosis will also be discussed.