Abstract: A roofing system (20) for a structure such as a building. The system (20) includes a roof deck (10), a plurality of panels (12) of an extruded alkenyl aromatic polymer foam above and adjacent the deck (10); and a substantially waterproof membrane (14), above and adjacent to the foam. The foam has an open cell content of 30 percent or more. The foam provides excellent mechanical support for the membrane (14), and is water resistant. The foam further has a high heat distortion temperature, and is substantially free of distortion at high service temperatures encountered in roofing systems. Further disclosed is a recovery roofing system employing the above foam. Further disclosed are processes for constructing a new roofing system and a recovery roofing system.