The importance of "size and scale" in nanoscience and engineering has been recognized by both scientists and science educators. A solid understanding of this concept is key to the learning of nanoscience. Students, however, have been reported to have considerable difficulty grasping this concept; yet little is known regarding their state of understanding. To address this knowledge gap, we conducted a series of studies that were aimed at exploring the different ways students conceive of "size and scale" in the context of undergraduate nanoscience and engineering courses. Informed by Variation Theory of Learning (Marton and Booth, 1997), we identified four major categories (with two sub-categories within each) of student conception--fragmented, linear, proportional, and logarithmic. These conception categories, together with the aspects of variation that characterize and distinguish them, are summarized in a typology. In addition to serving as a diagnostic tool to describe students' understanding, this typology can also be used to guide the development of instructional interventions that facilitate students to move toward a more sophisticated understanding of "size and scale." (Contains 8 figures and 1 note.)