Basements can be insulated from the outside or the inside.
Insulating the exterior wall with rigid boards of extruded polystyrene has the advantage of using the foundation as a thermal mass to store heat during winter. However, the insulation can potentially be damaged by pests and sunlight unless it is covered.
If you are planning to finish a basement, it might be more advantageous to insulate the interior walls.
The most durable and moisture resistant option is to use extruded polystyrene for the basement insulation, although it is more expensive than fiberglass. Another option is to frame the walls and install fiberglass batts, but this method has the potential for mold and moisture issues. In both cases, a gypsum board fire protection must cover the insulation system.
For more detailed basement insulation information see:
