Deep neural networks have been shown to be vulnerable to adversarial attacks. Typical attack strategies alter authentic data subtly so as to obtain adversarial samples that resemble the original but otherwise would cause a network's misbehavior such as a high misclassification rate. Various attack approaches have been reported, with some showing state-of-the-art performance in attacking certain networks. In the meanwhile, many defense mechanisms have been proposed in the literature, some of which are quite effective for guarding against typical attacks. Yet, most of these attacks fail when the targeted network modifies its architecture or uses another set of parameters and vice versa. Moreover, the emerging of more advanced deep neural networks, such as generative adversarial networks (GANs), has made the situation more complicated and the game between the attack and defense is continuing. This dissertation aims at exploring the venerability of the deep neural networks by investigating the mechanisms behind the success/failure of the existing attack and defense approaches. Therefore, several deep learning-based approaches have been proposed to study the problem from different perspectives. First, I developed an adversarial attack approach by exploring the unlearned region of a typical deep neural network which is often over-parameterized. Second, I proposed an end-to-end learning framework to analyze the images generated by different GAN models. Third, I developed a defense mechanism that can secure the deep neural network against adversarial attacks with a defense layer consisting of a set of orthogonal kernels. Substantial experiments are conducted to unveil the potential factors that contribute to attack/defense effectiveness. This dissertation also concludes with a discussion of possible future works of achieving a robust deep neural network.