Health professions training is mainly competency driven, with students’ and trainees’ learning and technical skill development regularly assessed, usually in terms of standardized outcomes. Yet, there are good ethical and clinical questions to ask about competency-based medical education, specifically about how schools’ and academic health centers’ curricula meaningfully motivate learning and skill development about social privilege, health equity, and structural determinants of patients’ health and health outcomes. This theme issue considers whether and to what extent skill development about, for example, the affective features of, say, coming to terms with one’s privilege is teachable and assessable in competency-based frameworks, especially when those frameworks have a history of excluding key perspectives. Critical pedagogies investigated herein suggest strategies for interrogating teaching and learning methods and curricular content that are socially, culturally, politically, and historically fraught.