Deep neural networks have achieved impressive experimental results in image classification, but can surprisingly be unstable with respect to adversarial perturbations, that is, minimal changes to the input image that cause the network to misclassify it. With potential applications including perception modules and end-to-end controllers for self-driving cars, this raises concerns about their safety. This lecture will describe progress with developing automated verification techniques for deep neural networks to ensure safety of their classification decisions with respect to image manipulations, for example scratches or changes to camera angle or lighting conditions, that should not affect the classification. The techniques exploit Lipschitz continuity of the networks and aim to approximate, for a given set of inputs, the reachable set of network outputs in terms of lower and upper bounds, in anytime manner, with provable guarantees. We develop novel algorithms based on games and global optimisation, and evaluate them on state-of-the-art networks.