In this chapter we explore and evaluate methods for trabecular bone characterization and osteoporosis diagnosis with increased interest in sparse approximations. We first describe texture representation and classification techniques, patch-based methods such as Bag of Keypoints, and more recent deep neural networks. Then we introduce the concept of sparse representations for pattern recognition and we detail integrative sparse analysis methods and classifier decision fusion methods. We report cross-validation results on osteoporosis datasets of bone radiographs and compare the results produced by the different categories of methods. We conclude that advances in the AI and machine learning fields have enabled the development of methods that can be used as diagnostic tools in clinical settings.