Summary: A general framework for the thermodynamics of open systems is presented. The theory is fundamentally based on the generalized balance of mass, which is enhanced by additional surface-flux and volume-source terms. The presentation highlights the influence of the enhanced mass balance on the remaining balance equations. To clarify the impact of the variable reference density, we introduce the notions of volume-specific and mass-specific formats. Particular attention is drawn to the fact that the mass-specific balance equations are free from explicit open-system contributions. They resemble the classical balance equations and can thus be evaluated in complete analogy to the closed-system case. Restrictions for the constitutive equations follow from the second law of thermodynamics, as illustrated for the particular model problem of thermo-hyperelasticity.