Used by jihadists everywhere from Paris and Brussels to the battlefields of Syria and Iraq, the dangerously unstable TATP has become the explosive of choice for the Islamic State group, which claimed the attacks in Barcelona and the seaside resort of Cambrils.
Investigators uncovered ingredients of the explosive at a house in the town of Alcanar, around 200 kilometres (120 miles) south of Barcelona, believed to be the terror cell's bomb-making factory.
Discovered at the end of the 19th century by a German chemist, TATP is a homemade explosive created by mixing precise quantities of acetone, oxygenated water and sulphuric, hydrochloric or nitric acid — all of which are easily available in high street stores.
Nail polish remover is essentially acetone, while oxygenated water is a commonly used disinfectant.
The mixture creates a coarse powder of white crystals that requires only a basic detonator to explode, triggering a huge blast of burning gas.
Jihadists have set up entire labs — at first backroom affairs, but increasingly reaching industrial levels — to produce TATP and other explosive materials in Syria and Iraq.
The UK-based Conflict Armament Research monitor said in a report last year that 51 companies had supplied the components needed to make homemade explosives at semi-industrial levels to IS.
The companies were spread across 20 countries, including Turkey and Russia, but also Belgium and the United States.
Detonators can be made with a thin metal tube filled with paste and linked to two electric wires that will spark and trigger a flame when connected.
But they can just as easily be bought ready made from a shop.
One of the attackers in the November 2015 bloodbath in Paris had bought a dozen pyrotechnic detonators at a fireworks store in the Paris region without raising the slightest suspicion.
Yet contrary to urban myth, more than a tutorial online is needed to learn how to put the ingredients together.
The most delicate part is adding the acid to the mixture, which lets off heat and can catch fire, but a simple mask is all that is normally needed for protection.
The volatility of the operation is perhaps illustrated by the fate of the suspects preparing the bombs in Alcanar, where they are believed to have accidentally sparked a detonation that killed at least two of them on the eve of the Barcelona van rampage.