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Résumé : Learning from non-stationary data streams and overcoming catastrophic forgetting still poses a serious challenge for machine learning research. Rather than aiming to improve state-of-the-art, in this work we provide insight into the limits and merits of rehearsal, one of continual learning's most established methods. We hypothesize that models trained sequentially with rehearsal tend to stay in the same low-loss region after a task has finished, but are at risk of overfitting on its sample memory, hence harming generalization. We provide both conceptual and strong empirical evidence on three benchmarks for both behaviors, bringing novel insights into the dynamics of rehearsal and continual learning in general. Finally, we interpret important continual learning works in the light of our findings, allowing for a deeper understanding of their successes.