Induced decision trees are an extensively-researched solution to classification tasks. For many practical tasks, the trees produced by tree-generation algorithms are not comprehensible to users due to their size and complexity. Although many tree induction algorithms have been shown to produce simpler, more comprehensible trees (or data structures derived from trees) with good classification accuracy, tree simplification has usually been of secondary concern relative to accuracy, and no attempt has been made to survey the literature from the perspective of simplification. We present a framework that organizes the approaches to tree simplification and summarize and critique the approaches within this framework. The purpose of this survey is to provide researchers and practitioners with a concise overview of tree-simplification approaches and insight into their relative capabilities. In our final discussion, we briefly describe some empirical findings and discuss the application of tree induction algorithms to case retrieval in case-based reasoning systems.