Signal processing offers a wide spectrum of theories, methods, and algorithms for addressing a variety of problems ranging from noise reduction, restoration, detection (of events or changes), spatiotemporal dynamics estimation, source localization, and pattern recognition. However, the classical assumptions (stationarity, linearity, etc.) usually do not apply in real situations. Recent advances, such as time-scale and time-frequency transforms, data fusion, long-range dependence, and higher order moments, do not always provide sufficiently robust solutions. In this article, the basic properties and generic features of biomedical signals are examined using a wide range of examples. Algorithmic results are presented to show not only the potential performance but also the limitations of the processing resources at our disposal. The last section describes and discusses signal matching, scenario recognition, and data fusion.