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Vertebral fractures, which are fractures of the bone in the spine, are the most common type of fracture in people aged 50 and older. These fractures are strongly associated with impaired quality of life and excess mortality. Accurate estimates of an individual's risk of vertebral fracture are necessary for better treatment and prevention of these fractures, but these estimates have remained elusive. This dissertation project seeks to fill gaps in knowledge that exist regarding a key prerequisite for developing better indicators of fracture risk: assessment of non-invasive methods for predicting deformation and failure mechanisms in the vertebra. The first part of this work focused on improving the performance of image-based finite element (FE) models in predicting the deformation and failure patterns that occur during vertebral fractures. These FE models are built from computed tomography (CT) images of a spine, and thus they are possible to use in a clinical setting for patient-specific predictions of vertebral fracture. Compared with currently used clinical methods, CT-based FE models have the advantage of integrating patient-specific geometry, image-based estimates of material properties, and physiological loading conditions to predict the mechanical behavior of the vertebra. However, recent findings suggest that poor estimation of material properties may be a major cause of prediction errors in these models. The first two studies in this dissertation therefore sought to determine how different constitutive models for bone tissue material properties influence the accuracy of the FE predictions of deformation and failure of the vertebra. One study compared two different yield criteria together with two constitutive relationships based on CT-measured density, and the other study tested the use of a constitutive relationship that accounts for microstructural anisotropy, rather than only density. In both studies, displacement fields throughout whole vertebral body measured experimentally in prior work were used as the ground truth in the calculation of prediction errors. We found that constitutive relationships based only on density are not sufficient when seeking accurate FE predictions of deformation fields in the vertebra. The second part of this work focused on deformation and failure mechanisms in a specific region of the vertebra: the vertebral endplate. The vertebral endplate is a thin, porous platform of mineralized tissue at the top and bottom boundaries of the vertebra where it connects with the intervertebral disc. Clinical observations have revealed that the vertebral fractures frequently occur in the region of the vertebral endplate. However, the mechanical behavior of this region is incompletely understood. We therefore sought to quantify the macroscale and microscale mechanical properties of the vertebral endplate. Four-point bend tests were conducted on specimens of the vertebral endplate to quantify the macroscale mechanical behavior and to determine associations between this behavior and composition. Subsequently, FE modeling of the bend tests and Baysesian optimization were used to identify the microscale material properties of the tissue within the vertebral endplate. We found that the macroscale properties of the vertebral endplate are moderately well predicted by density, including measures of density obtained from high-resolution CT scans. However, we also found wide variations in mechanical properties--in particular fracture strain--that were not associated with any of the measures of density or composition. Taken together, these results of these studies provide important data on the use of non-invasive measures of bone density and microstructure to predict vertebral deformation and failure. We find that, at multiple length scales, measures of density obtained from CT imaging, are only moderately beneficial in understanding and predicting vertebral mechanical behavior. Further work is required to develop and incorporate constitutive models that account for microstruture, not just density. This outcome, together with the quantitative measurements we provide on the accuracy of FE-based predictions of vertebral failure and the mechanical properties of the vertebral endplate, constitute critical milestones along the path towards robust estimation of the risk of vertebral fracture risk in clinical settings.