Some argue that biologically inspired algorithms are the future of solving difficult problems in computer science. Others strongly believe that the future lies in the exploration of mathematical foundations of problems at hand. The field of computer security tends to accept the latter view as a more appropriate approach due to its more workable validation and verification possibilities. The lack of rigorous scientific practices prevalent in biologically inspired security research does not aid in presenting bio-inspired security approaches as a viable way of dealing with complex security problems. This chapter introduces a biologically inspired algorithm, called the Self Organising Map (SOM), that was developed by Teuvo Kohonen in 1981. Since the algorithms inception it has been scrutinised by the scientific community and analysed in more than 4000 research papers, many of which dealt with various computer security issues, from anomaly detection, analysis of executables all the way to wireless network monitoring. In this chapter a review of security related SOM research undertaken in the past is presented and analysed. The algorithms biological analogies are detailed and the authors view on the future possibilities of this successful bio-inspired approach are given. The SOM algorithms close relation to a number of vital functions of the human brain and the emergence of multi-core computer architectures are the two main reasons behind our assumption that the future of the SOM algorithm and its variations is promising, notably in the field of computer security.