Coronal magnetic field models use photospheric field measurements as boundary condition to model the solar corona. We review in this paper the most common model assumptions, starting from MHD-models, magnetohydrostatics, force-free and finally potential field models. Each model in this list is somewhat less complex than the previous one and makes more restrictive assumptions by neglecting physical effects. The magnetohydrostatic approach neglects time-dependent phenomena and plasma flows, the force-free approach neglects additionally the gradient of the plasma pressure and the gravity force. This leads to the assumption of a vanishing Lorentz force and electric currents are parallel (or anti-parallel) to the magnetic field lines. Finally, the potential field approach neglects also these currents. We outline the main assumptions, benefits and limitations of these models both from a theoretical (how realistic are the models?) and a practical viewpoint (which computer resources to we need?). Finally we address the important problem of noisy and inconsistent photospheric boundary conditions and the possibility of using chromospheric and coronal observations to improve the models.