We present Saliency-driven Experience Replay - SER - a biologically-plausible approach based on replicating human visual saliency to enhance classification models in continual learning settings. Inspired by neurophysiological evidence that the primary visual cortex does not contribute to object manifold untangling for categorization and that primordial saliency biases are still embedded in the modern brain, we propose to employ auxiliary saliency prediction features as a modulation signal to drive and stabilize the learning of a sequence of non-i.i.d. classification tasks. Experimental results confirm that SER effectively enhances the performance (in some cases up to about twenty percent points) of state-of-the-art continual learning methods, both in class-incremental and task-incremental settings. Moreover, we show that saliency-based modulation successfully encourages the learning of features that are more robust to the presence of spurious features and to adversarial attacks than baseline methods. Code will be released upon acceptance.