The well-replicated observation that many people maintain mental health despite exposure to severe psychological or physical adversity has ignited interest in the mechanisms that protect against stress-related mental illness. Focusing on resilience rather than pathophysiology in many ways represents a paradigm shift in clinical-psychological and psychiatric research that has great potential for the development of new prevention and treatment strategies. More recently, research into resilience also arrived in the neurobiological community, posing nontrivial questions about ecological validity and translatability. Drawing on concepts and findings from transdiagnostic psychiatry, emotion research, and behavioral and cognitive neuroscience, we propose a unified theoretical framework for the neuroscientific study of general resilience mechanisms. The framework is applicable to both animal and human research and supports the design and interpretation of translational studies. The theory emphasizes the causal role of stimulus appraisal (evaluation) processes in the generation of emotional responses, including responses to potential stressors. On this basis, it posits that a positive (non-negative) appraisal style is the key mechanism that protects against the detrimental effects of stress and mediates the effects of other known resilience factors. Appraisal style is shaped by three classes of cognitive processes – positive situation classification, reappraisal, and interference inhibition – that can be investigated at the neural level. Prospects for the future development of resilience research are discussed.