In the past few years, significant progress has been made on deep neural networks (DNNs) in achieving human-level intelligence on several long-standing tasks. With broader deployment of DNNs on various applications, the concerns on its safety and trustworthiness have been raised, particularly after the fatal incidents of self-driving cars. Research to address these concerns is very active, with many papers released in the past few years. This survey paper is to conduct a review of the current research efforts on making DNNs safe and trustworthy, by focusing on four aspects, i.e., verification, testing, adversarial attack and defence, and interpretability. In total, we surveyed 178 papers, most of which were published in the most recent two years, i.e., 2017 and 2018.