After a general introduction on the kind of models and the use of models in the natural sciences, the main body of this paper reviews potential properties of structure based surface EMG (sEMG) models. The specific peculiarities of the categories (i) source description, (ii) motor unit structure, (iii) volume conduction, (iv) recording configurations and (v) recruitment and firing behaviour are discussed. For a specific goal, not all aspects conceivable have to be part of a model description. Therefore, finally an attempt is made to integrate the 'question level' and the 'model property level' in a matrix providing direction to the development and application of sEMG models with different characteristics and varying complexity. From this overview it appears that the least complex are models describing how the morphological muscle features are reflected in multi-channel EMG measurements. The most challenging questions in terms of model complexity are related to supporting the diagnosis of neuromuscular disorders.