With the development of the fifth-generation networks and artificial intelligence technologies, new threats and challenges have emerged to wireless communication systems, especially in cybersecurity. In this paper, we offer a review on attack detection methods involving deep learning techniques. Specifically, we first summarize fundamental problems of network security and attack detection and introduce several successful related applications using deep learning structures. We categorize deep learning methods and focus on attack detection methods built on different kinds of architectures, such as autoencoders, generative adversarial networks, recurrent neural networks, and convolutional neural networks. We also present some benchmark datasets and compare the performance of different approaches to show the current working state of attack detection methods using deep learning structures. Finally, we summarize the paper and discuss ways to improve the performance of attack detection with deep learning techniques.