The CLEVR dataset of natural-looking questions about 3D-rendered scenes has recently received much attention from the research community. A number of models have been proposed for this task, many of which achieved very high accuracies of around 97-99%. In this work, we study how systematic the generalization of such models is, that is to which extent they are capable of handling novel combinations of known linguistic constructs. To this end, we test models’ understanding of referring expressions based on matching object properties (such as e.g. “another cube that is the same size as the brown cube”) in novel contexts. Our experiments on the thereby constructed CLOSURE benchmark show that state-of-the-art models often do not exhibit systematicity after being trained on CLEVR. Surprisingly, we find that an explicitly compositional Neural Module Network model also generalizes badly on CLOSURE, even when it has access to the ground-truth programs at test time. We improve the NMN’s systematic generalization by developing a novel Vector-NMN module architecture with vector-valued inputs and outputs. Lastly, we investigate how much few-shot transfer learning can help models that are pretrained on CLEVR to adapt to CLOSURE. Our few-shot learning experiments contrast the adaptation behavior of the models with intermediate discrete programs with that of the end-to-end continuous models.