Despite daily observations of the Sun, many students continue to struggle with the mechanisms explaining its apparent motion. Even after formal instruction, students often develop only fragmentary understandings and construct alternative mental models. This study investigates these models in depth, to gain genuine insight into the knowledge structures students develop regarding the Sun’s apparent motion. We conducted individual task-based think-aloud interviews with 16-18-year-olds in which they articulated their mental models verbally, through drawings and by using three-dimensional materials. These explanations were then analyzed to determine whether the mental models included the essential elements, characteristics, and connections consistent with scientific understanding. The analysis showed that students often described individual aspects of the phenomenon correctly, but rarely provided adequate allocentric explanations. Missing components in their models were frequently supplemented with alternative ideas that clustered around five themes: cardinal directions, distance, orientation of Earth’s axis, lines of sight and sunrays, and the orientation of the Sun’s orbital plane. These themes, the variety within each, and the implications of our findings are discussed in detail.