The need to adaptively manage computer systems and networks so as to offer good Quality of Service (QoS) and Quality of Experience (QoE), with secure operation at relatively low levels of energy consumption is challenged by their sheer complexity and the wide variability of the workloads. A possible way forward is through self-awareness, whereby self-measurement and self-observation, together with on-line control mechanisms which operate adaptively to attain the required performance and QoE. We survey the premises for these ideas coming from Cognitive Science and Active Networks, and review recent work on self-aware computer systems and networks, including those that propose the use of Software Defined Networks as a means to implement these concepts. Then we provide some examples from the literature on self-aware systems to illustrate the performance gains that they can provide. Finally we detail an example system and its working algorithms to allow the reader to understand how such a system may be implemented. Measurements showing how it can react rapidly to changing network conditions regarding Quality of Service (QoS) and security are also presented. Some conclusions and suggestions for further work are also presented