This article describes some of the underlying conceptualizations that have gone into the work of the BEAR Center in the development of learning progressions. The core of all of these developments has been the construct map, which is the first building block in the BEAR Assessment System (BAS). After introducing the concept of a learning progression, the article summarizes the elements of the BAS, emphasizing the central concept of a construct map. The article then describes a series of several different ways to see the relationship between the idea of a construct map and the idea of a progression (which I call the "assessment structure"), and also gives illustrative examples from recent BEAR projects. The article then discusses some strengths and limitations of these conceptualizations, focusing on both educational and measurement issues. The article concludes with some general reflections. (Contains 11 figures.)