Deep neural networks (DNNs) have a wide range of applications, and software employing them must bethoroughly tested, especially in safety-critical domains. However, traditional software test coverage metricscannot be applied directly to DNNs. In this paper, inspired by the MC/DC coverage criterion, we proposea family of four novel test coverage criteria that are tailored to structural features of DNNs and their semantics. We validate the criteria by demonstrating that test inputs that are generated with guidance by ourproposed coverage criteria are able to capture undesired behaviours in a DNN. Test cases are generated using a symbolic approach and a gradient-based heuristic search. By comparing them with existing methods,we show that our criteria achieve a balance between their ability to find bugs (proxied using adversarial examples and correlation with functional coverage) and the computational cost of test input generation. Ourexperiments are conducted on state-of-the-art DNNs obtained using popular open source datasets, includingMNIST, CIFAR-10 and ImageNet.