The connection between the molecular-level structure of a substance and its macroscopic properties is a fundamental concept in chemistry. Students in college-level general and organic chemistry courses were interviewed to investigate how they used structure-property relationships to predict properties such as melting and boiling points. Although student difficulties in this area are well documented, they are usually classified as individual misconceptions. However our studies showed that student problems appear to arise from a complex interplay of problems involving a number of different sources: (1) models of phases/phase change, (2) use of representations, (3) language and terminology, and (4) use of heuristics in student reasoning. No two students used the same sets of ideas to perform the task at hand, and while we did see some recurrences of a single idea or heuristic, the ways that students combined them were different. We believe that, at least for high-level complex tasks such as determining structure-property relationships, student understanding is best understood as a set of loosely connected ideas, skills, and heuristics that are not well integrated. These are not single "misconceptions" that can be reconstructed in isolation. What is clear is that students who have done everything we ask of them, and who have earned high grades in chemistry courses are unable to address a core concept in chemistry. Typical assessments often mask the difficulties that students have with core concepts, since many students may correctly answer a question using heuristics, but have faulty reasoning. We recommend that instruction should include a scaffolded progression of ideas, and opportunities to construct and connect their understanding that will allow students to construct a more coherent framework from which to make predictions about the behavior of matter. (Contains 3 tables and 5 figures.)