We discuss different approaches to the challenge of robust object recognition under distribution shifts. We advocate a view of this challenge that is more closely informed by the problem of visual recognition, and which emphasizes dynamic model behaviour as opposed to centering the statistical properties of training and test distributions. We introduce an experimental setting geared towards developing models that can exhibit robust behaviour in a reliable and scalable manner. We refer to this requirement "systematic robustness", which involves excluding certain combinations of classes and image attributes are systematically during training. Unlike prior work which studies systematic generalisation in DNNs or their susceptibility to spurious correlations, we use synthetic operations and data sampling to scale such experiments up to large-scale naturalistic datasets.