The paper reviews the fundamental components of stochastic and motor-unit-based models of the surface electromyogram (SEMG). Stochastic models used in ergonomics and kinesiology consider the SEMG to be a stochastic process whose amplitude is related to the level of muscle activation and whose power spectral density reflects muscle conduction velocity. Motor-unit-based models for describing the spatio-temporal distribution of individual motor-unit action potentials throughout the limb are quite robust, making it possible to extract precise information about motor-unit architecture from SEMG signals recorded by multi-electrode arrays. Motor-unit-based models have not yet been proven as successful, however, for extracting information about recruitment and firing rates throughout the full range of contraction. The relationship between SEMG and force during natural dynamic movements is much too complex to model in terms of single motor units.