In the past, Vieille's law and minor modifications of it described sufficiently the linear burning rate of gun propellants which governs the design of charges by interior ballistic simulations. Recent developments to increase the performance led to new gun concepts and innovative propellants. These are the electrothermal-chemical gun, porous and foamed charges as well as formulations exhibiting a temperature independent burning. Vieille's law cannot fully meet experimental results in these cases. Approaches based on the heat flow equation in the solid energetic material give simplified formulas to extend the validity. These burning rate models have the ability to describe the experimentally determined burning behavior at least in a simplified or qualitative way. More sophisticated methods consider complex geometrical structures in the solid or take into account the actual progress in phase behavior and reaction kinetics of heterogeneous combustion. The dependence of the burning rate on initial temperature, on phase transitions, porous structure and gaseous reactions can be described.