A relatively popular use of Styrofoam is to carve out intricate patterns and then apply the sheets of Styrofoam to walls and other flats. There are many methods of carving out Styrofoam, the simplest being with a utility knife. Extreme caution must be taken when using sharp tools, etc. Another handy tool is a standard kitchen electric knife; though these are more popularly used for carving regular foam rubber versus Styrofoam.
Custom cutting tools are also available for cutting Styrofoam.
As you can see by the pattern of the cutting wire, this is being used to cut out crown molding. Using hotwire cutting tools are extremely efficient when cutting Styrofoam, but bring additional safety precautions to the table. First, they are very hot! Second, but more importantly, they must be used in well ventilated areas and may require wearing safety masks with specialized air filters. You’ll need to refer to the material data safety sheets as needed. http://www.hotwiredirect.com/products/hot-knife/