This chapter explores the use of mathematical modelling for the simulation and optimisation of microgeneration technologies. In the case of simulation this is to explore the performance of microgeneration technologies against user-defined performance criteria. In the case of optimisation, this is to identify an optimum solution against user-defined constraints. The discussion begins at the scale of modelling individual components within a microgeneration system and the operation of these systems within the home, then moves up to country-scale modelling of how microgeneration acts within the whole energy system and its impacts on national energy consumption and carbon emissions.