This study tests a hypothesized learning progression for the concept of energy. It looks at 14 specific ideas under the categories of (i) Energy Forms and Transformations; (ii) Energy Transfer; (iii) Energy Dissipation and Degradation; and (iv) Energy Conservation. It then examines students' growth of understanding within each of these ideas at three levels of increasing conceptual complexity. The basic level of the model focuses on simple energy relationships and easily observable effects of energy processes; the intermediate level focuses on more complex energy concepts and applications; and the advanced level focuses on still more complex energy concepts, often requiring an atomic/molecular model to explain phenomena. The study includes results from 359 distractor-driven, multiple-choice test items administered to over 20,000 students in grades 4 through 12 from across the U.S. Rasch analysis provided linear measures of student performance and item difficulty on the same scale. Results largely supported a model of students' growth of understanding that progresses from an understanding of forms and transformations of energy to energy transfer to conservation while also progressing along a separate dimension of cognitive complexity. An analysis of the current state of students' understanding with respect to the knowledge identified in the learning progression showed that elementary level students perform well in comparison to expectations but that middle and high school students' performance does not meet expectations. [This paper was published in the "Journal of Research in Science Teaching" v55 n1 p68-93 Jan 2018 (EJ1163319).]