Purpose Physician burnout is endemic across medical education and has numerous deleterious effects. Given the prevalence and negative effects of burnout, there is an urgent need to understand how residents experience and cope with stress and develop explanatory models that inform the development of more effective interventions. Method Using a qualitative, constructivist approach informed by grounded theory, the authors conducted semistructured interviews from March to April 2019, in which psychiatry residents were asked about their experiences of stress and how they coped. First- through fourth-year trainees at Zucker Hillside Hospital at Northwell Health, Glen Oaks, New York, were invited. Two authors independently and inductively coded deidentified transcripts. A constant comparative approach was used to analyze data and support construction of themes. Theoretic sufficiency was observed after 14 interviews. Results The authors constructed an explanatory model for how residents cope with stress and whether they tended toward burnout or wholehearted engagement. The model included 3 themes: self-care, work relationships, and meaning making. Self-care, including time spent with others, provided connection and belonging that bolstered physicians’ developing identities. Interpersonal relationships at work profoundly influenced the experience of residents. Positive peer and supervisor relationships enhanced confidence and perseverance. Negative role models and conflict engendered feelings of inadequacy. The ability to shift perspective and build meaning through examining moral values in the face of challenges was crucial for residents who reported success at coping with stress. Residents identified personal psychotherapy as an especially important strategy to facilitate meaning making. Conclusions These findings provide guidance for how residency programs may help residents cope with stress and move away from burnout toward wholehearted engagement. Strategies may include reducing barriers to self-care and to accessing help early in training, creating spaces that promote peer connection and providing training in addressing conflict, and facilitating engagement in meaning-making activities.