Executive summary : US use in Fallujah not actually illegal, but mainly because the US hasn't signed up to all the treaties that other countries have.
Key points :
What are the international conventions?
Washington is not a signatory to any treaty restricting the use of white phosphorus against civilians.
White phosphorus is covered by Protocol III of the 1980 Convention on Conventional Weapons, which prohibits its use as an incendiary weapon against civilian populations or in air attacks against enemy forces in civilian areas.
The US - unlike 80 other countries including the UK - is not a signatory to Protocol III.
What is the current furore about?
Critics say phosphorus bombs should not be used in areas where there is a risk they could cause serious burns or death to civilians.
Some have claimed the use of white phosphorus contravenes the 1993 Chemical Weapons Convention. This bans the use of any "toxic chemical" weapons which causes "death, harm or temporary incapacitation to humans or animals through their chemical action on life processes".
Professor Paul Rogers, of the University of Bradford's department of peace studies, told the BBC that white phosphorus could probably be considered a chemical weapon if deliberately aimed at civilians.