Title: Unifying Regularisation Methods for Continual Learning. Abstract: Continual Learning addresses the challenge of learning a number of different distributions sequentially. The goal of maintaining knowledge of earlier distributions without re-accessing them starkly conflicts with standard SGD training for artificial neural networks. An influential method to tackle this are so-called regularisation approaches. They measure the importance of each parameter for modelling a given distribution and subsequently protect important parameters from large changes. In the literature, three ways to measure parameter importance have been put forward and they have inspired a large body of follow-up work. Here, we present strong theoretical and empirical evidence that these three methods, Elastic Weight Consolidation (EWC), Synaptic Intelligence (SI) and Memory Aware Synapses (MAS), all approximate the Fisher Information. Only EWC intentionally relies on the Fisher, while the other two methods stem from rather different motivations. We find that for SI the relation to the Fisher -- and in fact its performance -- is due to a previously unknown bias. Altogether, this unifies a large body of regularisation approaches. It also provides the first theoretical explanation for  the effectiveness of SI- and MAS-based algorithms and offers theoretically justified versions of these algorithms. From a practical viewpoint, our insights offer computational speed-ups and uncover conditions needed for different algorithms to work.