What is the difference between fondant, gumpaste, & pastillage? And when do you use them?

Fondant is a simple sugar dough used to cover and decorate cakes. It can also be used to mold and cut out decorations, bows, etc and left to try. Gumpaste is similar to fondant, but has additional gum additives (different recipes use different gums in varying proportions) and dries, harder and faster than fondant. It is also more elastic than fondant, due to the gum additives, which makes it superior for flower making and other delicate items. Pastillage is is yet another sugar dough that dries EXTREMELY hard. It is also very strong and is usually used for structural items, such as cake bases, showpieces, etc. Pastillage is especially useful for making large items. Pastillage, in my experience, is the most unforgiving of these mediums as it begins to dry almost immediately upon contact with the air, but it's also very useful to have in your repertoire.