Currently, the network traffic control systems are mainly composed of the Internet core and wired/wireless heterogeneous backbone networks. Recently, these packet-switched systems are experiencing an explosive network traffic growth due to the rapid development of communication technologies. The existing network policies are not sophisticated enough to cope with the continually varying network conditions arising from the tremendous traffic growth. Deep learning, with the recent breakthrough in the machine learning/intelligence area, appears to be a viable approach for the network operators to configure and manage their networks in a more intelligent and autonomous fashion. While deep learning has received a significant research attention in a number of other domains such as computer vision, speech recognition, robotics, and so forth, its applications in network traffic control systems are relatively recent and garnered rather little attention. In this paper, we address this point and indicate the necessity of surveying the scattered works on deep learning applications for various network traffic control aspects. In this vein, we provide an overview of the state-of-the-art deep learning architectures and algorithms relevant to the network traffic control systems. Also, we discuss the deep learning enablers for network systems. In addition, we discuss, in detail, a new use case, i.e., deep learning based intelligent routing. We demonstrate the effectiveness of the deep learning-based routing approach in contrast with the conventional routing strategy. Furthermore, we discuss a number of open research issues, which researchers may find useful in the future.