Autonomic Computing is a concept that brings together many fields of computing with the purpose of creating computing systems that self-manage. In its early days it was criticised as being a “hype topic” or a rebadging of some Multi Agent Systems work. In this survey, we hope to show that this was not indeed ‘hype’ and that, though it draws on much work already carried out by the Computer Science and Control communities, its innovation is strong and lies in its robust application to the specific self-management of computing systems. To this end, we first provide an introduction to the motivation and concepts of autonomic computing and describe some research that has been seen as seminal in influencing a large proportion of early work. Taking the components of an established reference model in turn, we discuss the works that have provided significant contributions to that area. We then look at larger scaled systems that compose autonomic systems illustrating the hierarchical nature of their architectures. Autonomicity is not a well defined subject and as such different systems adhere to different degrees of Autonomicity, therefore we cross-slice the body of work in terms of these degrees. From this we list the key applications of autonomic computing and discuss the research work that is missing and what we believe the community should be considering.