Resilience is considered to be the process by which individuals demonstrate more positive outcomes than would be expected, given the nature of the adversity experienced. We propose that a cognitive approach has the potential to guide studies investigating the relationships between adversity, stress, and resilience. We outline a preliminary cognitive model of resilience in order to facilitate the application of cognitive approaches to the investigation of resilience in the face of adversity. We argue that the situationally appropriate application of flexibility or rigidity in affective-cognitive systems is a key element in promoting resilient responses. We propose that this mapping of cognitive processing can be conceptualised as being undertaken by an overarching mapping system, which serves to integrate information from a variety of sources, including the current situation, prior experience, as well as more conscious and goal-driven processes. We propose that a well-functioning mapping system is an integral part of the cognitive basis for resilience to adversity. Our preliminary model is intended to provide an initial theoretical framework to guide research on the development of cognitive functions that are considered to be important in the resilience process.