We present the fundamental equations which govern the physics of quiescent solar prominences. The mechanical equilibrium of prominences is described by the equations of magneto-hydrostatics. The radiative properties of the structures have to be modelled by non-LTE equations. In addition one has to prescribe the energetics of the cool prominence material in the coronal environment. The magneto-hydrodynamic equations allow us to construct 1D slab and 2D thread models. We then also discuss the aspects of magnetic dips. Furthermore, modern techniques of solving the complex set of non-LTE radiative transfer equations are described in some detail. Finally, new models resulting from a combination of magneto-hydrostatics and radiative transfer are outlined and their relevance for observations is discussed.