In this paper, we present a survey of deep learning approaches for cyber security intrusion detection, the datasets used, and a comparative study. Specifically, we provide a review of intrusion detection systems based on deep learning approaches. The dataset plays an important role in intrusion detection, therefore we describe 35 well-known cyber datasets and provide a classification of these datasets into seven categories; namely, network traffic-based dataset, electrical network-based dataset, internet traffic-based dataset, virtual private network-based dataset, android apps-based dataset, IoT traffic-based dataset, and internet-connected devices-based dataset. We analyze seven deep learning models including recurrent neural networks, deep neural networks, restricted Boltzmann machines, deep belief networks, convolutional neural networks, deep Boltzmann machines, and deep autoencoders. For each model, we study the performance in two categories of classification (binary and multiclass) under two new real traffic datasets, namely, the CSE-CIC-IDS2018 dataset and the Bot-IoT dataset. In addition, we use the most important performance indicators, namely, accuracy, false alarm rate, and detection rate for evaluating the efficiency of several methods.