The research reported in this article represents a systematic, multi-year investigation of student understanding of the behavior of bipolar junction transistor circuits using a variety of different tasks to isolate and probe key aspects of transistor circuit behavior. The participants in this study were undergraduates enrolled in upper-division physics electronics courses at three institutions, as well as undergraduates in upper-division engineering electronics courses at one of the institutions. Findings from this research indicate that many students have not developed a robust conceptual understanding of the functionality of bipolar junction transistors circuits even after all relevant instruction. Most notably, when asked to analyze the impact of a transistor circuit on input signals, students frequently applied reasoning appropriate for an analysis of the circuit's dc bias behavior. However, students often displayed knowledge of fundamental transistor behavior when responding to more targeted questions. This article provides insight into student thinking about transistor circuits, describing the most prevalent conceptual and reasoning difficulties identified and discussing some important implications for instruction.