Deep learning has led to rapid progress being made in the field of machine learning and artificial intelligence, leading to dramatically improved solutions of many challenging problems such as image understanding, speech recognition, and control systems. Despite these remarkable successes, researchers have observed some intriguing and troubling aspects of the behaviour of these models. A case in point is the presence of adversarial examples which make learning based systems fail in unexpected ways. Such behaviour and the difficulty of interpreting the behaviour of neural networks is a serious hindrance in the deployment of these models for safety-critical applications. In this talk, I will review the challenges in developing models that are robust and explainable and discuss the opportunities for collaboration between the formal methods and machine learning communities.