This paper describes the main features and the formal derivation of the environmental multi-sector DSGE model EMuSe. In addition to the closed-economy flexible-price benchmark model, an extension with nominal price rigidities and an open-economy version are presented. Selected applications of the model variants illustrate the main transmission channels in EMuSe. Together with the technical documentation, we provide the program codes to replicate the model applications as well as the EMuSe Calibration Toolkit.