What's the best way to cut expanded foam or polystyrene when modelling?

There are a number of ways to cut expanded foam or polystyrene when modelling, but which way is best?

As with many modelling techniques, the answer is subjective and what may be right for one modeller may not be for another. When it comes to cutting expanded foam or polystyrene, some modellers like to use a hobby knife or saw whilst others prefer to use a purpose-built hot wire tool. Both methods have their merits, but it's generally accepted that hot wire cutters offer cleaner cuts with less mess.