The functional purpose of all incendiary munitions, from historical Greek fire to modern day fuel-air bombs, is to ignite a robustly burning fire across a wide swath of the target area. To that end, modern day incendiary munitions employ a variety of different flammable materials.
Napalm is simply gasoline mixed with some sort of thickening agent. The thickening agent is meant to render the gasoline more viscous and glue-like so that it sticks to surfaces around the detonation site as it burns. Initially, the military used sodium palmitrate as its thickening agent (hence the name, Na-palm); more modern napalm employs polystyrene plastic beads as a thickener.
Napalm has been used both as a conventional incendiary weapon—attacking flammable military and civilian targets—and as a defoliant in the Vietnam war. The United States military used massive Napalm raids to clear away entire forests in order to deny its enemies refuge.
Flammable metals like the ones listed below are extremely useful in incendiary munitions because they burn so readily, durably, and intensely (i.e. at very high temperatures).
Depleted Uranium is especially useful because it can function both as a mechanically useful shell casing, by virtue of its high density, and (once the weapon is detonated) as a fiercely burning incendiary.
Thermite is a mixture of iron oxide (basically, rust) and aluminum; it is among the most widely used incendiary materials. The thermite reaction is as follows: Fe2O3 + 2Al → Al2O3 + 2Fe.
An unusual choice, due to its high cost.
White phosphorus is a solid which burns readily in air. Iit can be safely handle under water, but will burst into intense flame once dry. Phosphorus dispersed by high explosives has tremendous potential to cause injury, often embedding itself (in small pieces) in the skin of its victims and continuing to burn.
Fuel Air Explosives
These weapons disperse a large amount of flammable hydrocarbon (e.g. octane, ethylene) in aerosol form prior to detonation. As a result, the detonation of the weapon creates a massive fireball—consuming large amounts of target materials and breathable oxygen at the same time.