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This survey presents a comprehensive overview of machine learning methods for cybersecurity intrusion detection systems, with a specific focus on recent approaches based on deep learning (DL). The review analyzes recent methods with respect to their intrusion detection mechanisms, performance results, and limitations as well as whether they use benchmark databases to ensure a fair evaluation. In addition, a detailed investigation of benchmark datasets for cybersecurity is presented. This article is intended to provide a road map for readers who would like to understand the potential of DL methods for cybersecurity and intrusion detection systems, along with a detailed analysis of the benchmark datasets used in the literature to train DL models.