We report on a multi-year, multi-institution study to investigate students' reasoning about energy in the context of quantum tunneling. We use ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunneling through a square barrier are particularly common. Students often state that tunneling particles lose energy while tunneling. When sketching wavefunctions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical and graphical models of quantum tunneling. As part of a curriculum in quantum physics, we have developed instructional materials designed to help students develop a more robust and less inconsistent picture of tunneling, and present data suggesting that we have succeeded in doing so.