Recently, scientists have shifted their focus from studying psychological resilience as a single, isolated construct (e.g. attribute or outcome) to studying it as a dynamic process encompassing a number of temporally related elements. Models depicting this process explain why some people adapt to stressor exposure, whereas others do not. To date, these process models did not sufficiently explain how people adapt differently to a stressor. To address this issue, we developed a new model of psychological resilience, called the Psychological Immunity-Psychological Elasticity (PI-PE) model. The aim of this article is to clarify this model and to discuss its added value. First, we explain how we derived the PI-PE model from the literature regarding both the crucial elements in any resilience process model and the (mal)adaptive outcomes following stressful events. Secondly, we describe the different elements that make up the model. Characteristic of the PI-PE model is that it distinguishes between two pathways of psychological resilience–psychological immunity and psychological elasticity–with four adaptive outcomes, namely sustainability, recovery, transformation and thriving. To explain how people arrive at these different outcomes, we argue that two consecutive mechanisms are critical in these pathways: tolerance and narrative construction. Taken as a whole, the PI-PE model presents a comprehensive framework to inspire both research and practice. It explains how the process of psychological resilience works differently for different people and how to support individuals in their process towards successfully and differently adapting to stressors (download full article).