Science education involves learning about phenomena at three levels: concrete (facts and generalizations), conceptual (concepts and theories), and metaconceptual (epistemology) (Snir et al. in "J Sci Educ Technol" 2(2):373-388, 1993). Models are key components in science, can help build conceptual understanding, and may also build metaconceptual understanding. Technology can transform teaching and learning by turning models into interactive simulations that learners can investigate. This paper identifies four characteristics of models and simulations that support conceptual learning but misconstrue models and science at a metaconceptual level. A historical models combine the characteristics of several historical models; they conveniently compile ideas but misrepresent the history of science (Gilbert in "Int J Sci Math Educ" 2(2):115-130, 2004). Teleological models explain behavior in terms of a final cause; they can lead to useful heuristics but imply purpose in processes driven by chance and probability (Talanquer in "Int J Sci Educ" 29(7):853-870, 2007). Epistemological overreach occurs when models or simulations imply greater certainty and knowledge about phenomena than warranted; conceptualizing nature as being well known (e.g., having a mathematical structure) poses the danger of conflating model and reality or data and theory. Finally, models are inevitably ontologically impoverished. Real-world deviations and many variables are left out of models, as models' role is to simplify. Models and simulations also lose much of the sensory data present in phenomena. Teachers, designers, and professional development designers and facilitators must thus navigate the tension between conceptual and metaconceptual learning when using models and simulations. For each characteristic, examples are provided, along with recommendations for instruction and design. Prompts for explicit reflective activities around models are provided for each characteristic.