We have been studying the learning of compositional hierarchies in predictive models, an area we feel is significantly underrepresented in machine learning. The aim in learning such models is to scale up automatically from fine-grained to coarser representations by identifying frequently occurring repeated patterns, while retaining the ability to make predictions based on the statistica] regularities exhibited by these patterns. Our hierarchical learning begins with data consisting of discrete symbols and can be viewed as a method of grounding high-level concepts in terms of their lower-level parts, which are themselves grounded in raw, environmental signals by other means. This short paper discusses the relationship between hierarchy learning and the learning of low-level grounded representations and also very briefly describes one of our systems for compositional hierarchy learning. A much more detailed discussion, including an extensive literature review, can be found in (Pfleger 2000).