While ground truth depth data remains hard to obtain, self-supervised monocular depth estimation methods enjoy growing attention. Much research in this area aims at improving loss functions or network architectures. Most works, however, do not leverage self-supervision to its full potential. They stick to the standard closed world train-test pipeline, assuming the network parameters to be fixed after the training is finished. Such an assumption does not allow to adapt to new scenes, whereas with self-supervision this becomes possible without extra annotations.In this paper, we propose a novel self-supervised Continuous Monocular Depth Adaptation method (CoMoDA), which adapts the pretrained model on a test video on the fly. As opposed to existing test-time refinement methods that use isolated frame triplets, we opt for continuous adaptation, making use of the previous experience from the same scene. We additionally augment the proposed procedure with the experience from the distant past, preventing the model from overfitting and thus forgetting already learnt information.We demonstrate that our method can be used for both intra-and cross-dataset adaptation. By adapting the model from train to test set of the Eigen split of KITTI, we achieve state-of-the-art depth estimation performance and surpass all existing methods using standard architectures. We also show that our method runs 15 times faster than existing test-time refinement methods.