A surface electromyogram (sEMG) contains information about physiological and morphological characteristics of the active muscle and its neural strategies. Because the electrodes are situated on the skin above the muscle, the sEMG is an easily obtainable source of information. However, different combinations of physiological and morphological characteristics can lead to similar sEMG signals and sEMG recordings contain noise and other artefacts. Therefore, many sEMG signal processing methods have been developed and applied to allow insight into neuromuscular physiology. This paper gives an overview of important advances in the development and applications of sEMG signal processing methods, including spectral estimation, higher order statistics and spatio-temporal processing. These methods provide information about muscle activation dynamics and muscle fatigue, as well as characteristics and control of single motor units (conduction velocity, firing rate, amplitude distribution and synchronization).