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Compositional and relational learning is a hallmark of human intelligence, but one which presents challenges for neural models. One difficulty in the development of such models is the lack of benchmarks with clear compositional and relational task structure on which to systematically evaluate them. In this paper, we introduce an environment called ConceptWorld, which enables the generation of images from compositional and relational concepts, defined using a logical domain specific language. We use it to generate images for a variety of compositional structures: 2x2 squares, pentominoes, sequences, scenes involving these objects, and other more complex concepts. We perform experiments to test the ability of standard neural architectures to generalize on relations with compositional arguments as the compositional depth of those arguments increases and under substitution. We compare standard neural networks such as MLP, CNN and ResNet, as well as state-of-the-art relational networks including WReN and PrediNet in a multi-class image classification setting. For simple problems, all models generalize well to close concepts but struggle with longer compositional chains. For more complex tests involving substitutivity, all models struggle, even with short chains. In highlighting these difficulties and providing an environment for further experimentation, we hope to encourage the development of models which are able to generalize effectively in compositional, relational domains.