Modern Guatemala's claim is essentially inherited from the earlier and much larger, pre-Independence territorial block which was handily also known as Guatemala. (or rather the Captaincy General of...)
The Chapines continue to have their acquisitive eye on some 12,700 square kilometres of Belizean soil - more than half of the former British colony's total territory.
On Monday both countries signed an agreement in Washington DC stating that, pending referenda on each side, they would refer this matter to the International Court of Justice in the Hague.
The background to this dispute is indeed a little complicated. Belize was granted a quickie divorce from the UK in 1981 at a time when the Guatemalan army was too busy murdering its own citizens to do much in the line of effective sabre-rattling.
Back in the nineteenth century a formal treaty between Britain and Guatemala ceded the territory soon to be known as British Honduras to Her Majesty, just so long as Her Majesty went on to build Guatemala a nice new road linking their capital to the Atlantic. The continuing absence of this road suddenly came to the attention of the dictator Jorge Ubico in 1931...just before he gave away the publicly-funded railway he'd built instead to the United Fruit Company. Time to reassert that claim he must have thought...
It's hoped that the OAS-mediated 'special agreement' is the first step towards a definitive solution.
UPDATE: Somehow I find it hard to see how Guatemala won't get something out of this. Belize's de facto position is strong - it has 27 years behind it as an independent nation with a separate cultural and indeed political identity. But there seems little doubt that Britain defaulted on its treaty obligations and that therefore Guatemala's de iure position is also strong. The north and west of Belize are increasingly Hispanic in outlook too and perhaps look more to Central America than the Caribbean. If not compensation of some kind, I'd expect to see a more crinkly border once the ICJ has passed its judgment.