In this review, recent advances on the measurement and modeling of elastic properties of cortical and trabecular bone are presented. Bone is a multifunctional material which among its other functions serves as a support for other tissues in the body. As a structural material it is stiﬀ, strong, tough, lightweight and is adaptable. Its excellent mechanical properties are due to its complex, composite and hierarchical structure. In this paper, we outline the experimental approaches that have been used to characterize bone’s structure, composition and elastic properties at several diﬀerent length scales. Then, we discuss diﬀerent modeling approaches that have been employed to compute bone’s elastic moduli. We conclude by discussing the challenges and open issues in this area. Analysis of bone is of importance in orthopedics. Also, gained knowledge on bone can be used by engineers to design new bioinspired composit materials for a wide range of engineering applications.