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From tiny pacemaker chips to aircraft collision avoidance systems, the state-of-the-art Cyber-Physical Systems (CPS) have increasingly started to rely on Deep Neural Networks (DNNs). However, as concluded in various studies, DNNs are highly susceptible to security threats, including adversarial attacks. In this paper, we first discuss different vulnerabilities that can be exploited for generating security attacks for neural network-based systems. We then provide an overview of existing adversarial and fault-injection-based attacks on DNNs. We also present a brief analysis to highlight different challenges in the practical implementation of adversarial attacks. Finally, we also discuss various prospective ways to develop robust DNN-based systems that are resilient to adversarial and fault-injection attacks.