A great deal of attention has been given to deep learning over the past several years, and new deep learning techniques are emerging with improved functionality. Many computer and network applications actively utilize such deep learning algorithms and report enhanced performance through them. In this study, we present an overview of deep learning methodologies, including restricted Bolzmann machine-based deep belief network, deep neural network, and recurrent neural network, as well as the machine learning techniques relevant to network anomaly detection. In addition, this article introduces the latest work that employed deep learning techniques with the focus on network anomaly detection through the extensive literature survey. We also discuss our local experiments showing the feasibility of the deep learning approach to network traffic analysis.