This article presents a review of signals used for measuring physiology and activity during sleep and techniques for extracting information from these signals. We examine both clinical needs and biomedical signal processing approaches across a range of sensor types. Issues with recording and analysing the signals are discussed, together with their applicability to various clinical disorders. Both univariate and data fusion (exploiting the diverse characteristics of the primary recorded signals) approaches are discussed, together with a comparison of automated methods for analysing sleep.