It is a dispute which has pitted Morocco against the Polisario Front, an armed nationalist movement which formed the Sahrawi Arab Democratic Republic after the former colonial power Spain, pulled out of the region.
Supported by Algeria, the government in exile is headquartered in Tindouf.
King Hassan the Second of Morocco called on 350,000 of his subjects to march in 1975 – the so-called Green March – which put extra pressure on Spain to sign the Madrid accords, carving up Western Sahara.
At the time of the pull out, Spain handed the northern and central parts of Western Sahara to Morocco – the south went to Mauritania.
The Polisario Front waged a guerilla war against both.
In 1979, Mauritania signed a peace accord with the Polisario Front, and left.
But Morocco’s forces gave Rabat control over more than a quarter of a million square kilometres of territory.
The armed conflict lasted until a UN ceasefire came into force in 1991, with a mission to set up a referendum – one of the principal demands of the Polisario Front.
Rabat opposed any vote in the territory. Western Sahara is rich in phosphates – and Morocco is one of the world’s main exporters.
The fishing industry is another major resource, providing enough fish to supply the entire Moroccan kingdom.
But an end to the conflict still seems a long way off.
Talks in Al-Ayoun, Marrakesh, New York, London, Lisbon and Houston all failed.
Morocco, the Polisario Front, Algeria and Mauritania have to get round the same table to find a solution for the only African territory without a settled post-colonial administration.