We consider exponential decay of energy for the damped wave equation on tori. When the damping is continuous, the geometric control condition is necessary and sufficient. A recent result by N. Burq and P. Gérard adapts this condition to the framework of two-dimensional tori and discontinuous, polygon-shaped dampings. We will discuss their result and give some generalizations and (untechnical) sketches of proof on higher-dimensional tori.