Note on terminology
From the open literature it appears that some experts draw a distinction between the terms thermobaric weapon and fuel-air explosive based on the primary intended effects: "thermobaric" relating to closed-zone convection or air displacement as the primary objective, and "fuel-air" for use as area-denial or "daisy cutter"-like ordnance through blast and combustion, in a role somewhat similar to that of cluster bomb weapons. Other sources use "fuel-air" as the general case, subsuming "thermobaric" as previously detailed; still others use the two terms interchangeably. The term "thermobaric" appears to be of Russian/Soviet origin.
The blast wave destroys unreinforced buildings and equipment and kills and injures personnel. The antipersonnel effect of the blast wave is more severe in foxholes, on personnel with body armor, and in "stiff" enclosed spaces such as caves, buildings, and bunkers.
The overpressure within the detonation can reach 3 MPa (430 psi) and the temperature can be 2,500 - 3,000°C. Outside the cloud the blast wave travels at over 3 km/s. This blast wave leaves behind a vacuum. This vacuum then pulls in loose objects. Perhaps more seriously, it draws in the unexploded burning fuel to create almost complete penetration of all non-airtight objects within the blast radius, which are then incinerated. Asphyxiation and internal damage can also occur to personnel outside the highest blast effect zone, e.g. in deeper tunnels, as a result of the blast wave, the heat, or the following air draw.
The effects produced by FAEs (a long high duration pressure and heat impulse) are often likened to the effects produced by low-yield nuclear weapons, but without the problems of radiation--though this is inexact; for all current and foreseen subkiloton yield nuclear weapon designs, prompt radiation effects predominate, producing some secondary heating--very little of the nominal yield is actually delivered as blast. The significant injury dealt by either weapon on a targeted population is nonetheless great.
Some fuels used, such as ethylene oxide and propylene oxide, are highly toxic.
A device using such fuels is very dangerous even if the fuel fails to ignite; the device then becomes essentially a chemical weapons system.
Arguably, the use of flamethrowers in the trench warfare of World War I (the flamethrower was a German invention) could constitute the first use of a primitive "vacuum bomb", in that they could suffocate people protected from the direct weapon effects inside a pillbox or bunker. Other such effects were seen to occur in the firestorms at Dresden and elsewhere.
In the form that they exist today, these devices (then dubbed Fuel-Air Munitions) have been said to have been developed in the 1960s and used by the United States during the Vietnam War to destroy Viet Cong tunnels, clear forest for helicopter landing sites and to clear mine fields. However, it is not clear that this is entirely the case; in particular, the very large parachute-delivered "Daisy Cutter" bomb used for this purpose was suspected to have been such a weapon but the current published details indicate that it was not (it seems to be filled with a mixture of ammonium nitrate and jet fuel instead). FAMs are certainly in published literature available to English-speaking readers by the mid-1970s (Cite to come).
The Soviet armed forces also developed FAE weapons, including thermobaric warheads for shoulder-launched RPGss (RPO-A Shmel Bumblebee). Russian forces have a wide array of these weapons () and reportedly used them against Chinese forces in a 1969 border conflict, and certainly used them in Afghanistan and in Chechnya.
An FAE system from Israel was developed for minefield clearing. The system uses a small rocket propelled thermobaric charge which explodes over the minefield and activates exposed or buried mines. The system was developed for combat and peacekeeping uses, and due to its limited effect, have no collateral damage.