This paper presents the results of the work carried out by the CALAGUA Group on Mathematical Modelling of Biological Treatment Processes: the Biological Nutrient Removal Model No.1. This model is based on a new concept for dynamic simulation of wastewater treatment plants: a unique model can be used to design, simulate and optimize the whole plant, as it includes most of the biological and physico-chemical processes taking place in all treatment operations. The physical processes included are: settling and clarification processes (flocculated settling, hindered settling and thickening), volatile fatty acids elutriation and gas-liquid transfer. The chemical interactions included comprise acid-base processes, where equilibrium conditions are assumed. The biological processes included are: organic matter, nitrogen and phosphorus removal; acidogenesis, acetogenesis and methanogenesis. Environmental conditions in each operation unit (aerobic, anoxic or anaerobic) will determine which bacterial groups can grow. Thus, only the model parameters related to bacterial groups able to grow in any of the operation units of a specific WWTP will require calibration. One of the most important advantages of this model is that no additional analysis with respect to ASM2d is required for wastewater characterization. Some applications of this model have also been briefly explained in this paper.