Nowadays, there is a huge and growing concern about security in information and communication technology among the scientific community because any attack or anomaly in the network can greatly affect many domains such as national security, private data storage, social welfare, economic issues, and so on. Therefore, the anomaly detection domain is a broad research area, and many different techniques and approaches for this purpose have emerged through the years. In this study, the main objective is to review the most important aspects pertaining to anomaly detection, covering an overview of a background analysis as well as a core study on the most relevant techniques, methods, and systems within the area. Therefore, in order to ease the understanding of this survey’s structure, the anomaly detection domain was reviewed under five dimensions: (1) network traffic anomalies, (2) network data types, (3) intrusion detection systems categories, (4) detection methods and systems, and (5) open issues. The paper concludes with an open issues summary discussing presently unsolved problems, and final remarks.