The chapter describes visual classification by a hierarchy of semantic fragments. In fragment-based classification, objects within a class are represented by common sub-structures selected during training. The chapter describes two extensions to the basic fragment-based scheme. The first extension is the extraction and use of feature hierarchies. We describe a method that automatically constructs complete feature hierarchies from image examples, and show that features constructed hierarchically are significantly more informative and better for classification compared with similar non-hierarchical features. The second extension is the use of so-called semantic fragments to represent object parts. The goal of a semantic fragment is to represent the different possible appearances of a given object part. The visual appearance of such object parts can differ substantially, and therefore traditional image similarity-based methods are inappropriate for the task. We show how the method can aut...