To date, attempts to decipher proto-Elamite, a 5000-year-old writing system developed in what is now Iran, have failed, but academics at Oxford University may be close to a breakthrough, reports the BBC (in this article).
Over a thousand clay tablets inscribed with the writing survive, but, even though other ancient writing systems, such as ancient Egyptian and Sumerian, have been deciphered, it has proved very difficult to understand proto-Elamite. One reason for this is that no bilingual texts have been found (and it was the discovery of the bilingual Rosetta Stone that was the key to deciphering ancient Egyptian hieroglyphics - see this old post). Another reason is that there seem to be many errors in the writing, making it difficult to spot patterns.
The reason that the article predicts a breakthrough is that a new machine now exists which will 'read' the texts more clearly and make the markings more visible. Researcher Dr Jacob Dahl took the machine over to the Louvre museum in Paris, where there is a significant collection of the tablets.
Dr Dahl may not fully understand most of the writing, but he has gleaned enough to give an idea of the society that used the writing system. He can tell that the clay tablets mostly relate to accounting or trading matters (early texts often do - the Rosetta Stone text contains information about taxes). The society was hierarchical with the masses at the bottom subsisting on meagre diets. The upper echelons may have had a life expectancy similar to today's, according to Dr Dahl.
Here is the BBC piece with a picture of a tablet showing the writing.