The search for a measure of anaesthesia derived from the electroencephalogram (EEG) and evoked potentials (EPs) almost inevitably involves processing of the data by a computer. Digital signal processing is a major area of scientific research, and the purpose of this chapter is to outline some of the most important issues, to review past research, and to assess the possible approaches to the problem. The first section sets out the objectives viewing this as a system modelling problem. The following sections discuss the principal modelling techniques and techniques for determining the level of awareness from model parameters. The rest of the paper is a review of the applications of such methods, including both published results and an assessment of future potential.