Researchers and clinicians recognize that many unsolved medical problems are due to the application of conventional mathematics methods to describe biological complex systems. More recently, a different approach based on nonlinear dynamics, chaos and complexity has been considered, which recognizes irregularity, subjectivity and uncertainty as intrinsic and fundamental. Complexity is a property of every system that quantifies the amount of structured information. We investigate the use of complexity measures in biological signals, in particular will emphasise the usefulness of compression as a complexity measure. Entropy has been widely used in the area; however few studies consider compression as a measure of complexity. In this talk we will give strong evidence that compression should also be used as a useful measure of complexity in biological signals, in particular we used it with success in a fetal heart rate data set.