In this review article, we aim at analysing the role of stress in addiction and relapse. In order to do so, we first offer a summary of the findings from affective neuroscience trying to understand compulsive reward-seeking behaviours. These behaviours are characterised by an imbalance between the considerable amount of effort an individual is willing to mobilise to obtain a reward and the comparatively little pleasure that is felt once the reward is obtained and consumed. We illustrate how the neuropsychological mechanisms underlying these behaviours might play an important role in substance addiction and in particular for stress-induced relapse. We then review evidence suggesting that a personalised health approach would be particularly beneficial in order to better understand the role of stress in addiction and relapse in humans. More specifically, observing individual differences during distinct forms of learning (Pavlovian, habitual and goal-directed learning) might represent a very promising way to identify risk profiles for compulsive reward-seeking behaviours, addiction, and vulnerabilities to relapse under stress.