With the growing rates of cyber-attacks and cyber espionage, the need for better and more powerful intrusion detection systems (IDS) is even more warranted nowadays. The basic task of an IDS is to act as the first line of defense, in detecting attacks on the internet. As intrusion tactics from intruders become more sophisticated and difficult to detect, researchers have started to apply novel Machine Learning (ML) techniques to effectively detect intruders and hence preserve internet users' information and overall trust in the entire internet network security. Over the last decade, there has been an explosion of research on intrusion detection techniques based on ML and Deep Learning (DL) architectures on various cyber security-based datasets such as the DARPA, KDDCUP'99, NSL-KDD, CAIDA, CTU-13, UNSW-NB15. In this research, we review contemporary literature and provide a comprehensive survey of different types of intrusion detection technique that applies Support Vector Machines (SVMs) algorithms as a classifier. We focus only on studies that have been evaluated on the two most widely used datasets in cybersecurity namely: the KDDCUP'99 and the NSL-KDD datasets. We provide a summary of each method, identifying the role of the SVMs classifier, and all other algorithms involved in the studies. Furthermore, we present a critical review of each method, in tabular form, highlighting the performance measures, strengths, and limitations of each of the methods surveyed.