Based on the analysis of available research on students' alternative conceptions about the particulate nature of matter, we identified basic implicit assumptions that seem to constrain students' ideas and reasoning on this topic at various learning stages. Although many of these assumptions are interrelated, some of them seem to change or lose/gain strength independently from one another. Overlapping or competing presuppositions about the structure, properties, and dynamics of matter may be able to coexist at any given level, particularly at intermediate stages of expertise. Our results allowed us to suggest common paths in the transition from nave through novice to expert along relevant dimensions related to the structure and properties of chemical substances. The identification of these cognitive constraints provides a useful framework that educators can use to better understand and even predict many of their students' learning difficulties. It can also assist in the design and organisation of learning experiences and assessment tools that recognise and take advantage of the most likely trajectories towards expertise (learning progressions) followed by many students. (Contains 1 figure.)