The Elamite language is a historically attested, but undeciphered language historically used in Southwestern Iran from about 2600 BCE to 330 BCE. One not widely accepted theory supposes that it is ancestral to the Dravidian languages of South Asia. But, the leading view is that it is a language isolate. The linked Wikipedia article about this language notes that:
A sizeable number of Elamite lexemes are known from the trilingual Behistun inscription and numerous other bilingual or trilingual inscriptions of the Achaemenid Empire, in which Elamite was written using Elamite cuneiform (circa 400 BC), which is fully deciphered. An important dictionary of the Elamite language, the Elamisches Wörterbuch was published in 1987 by W. Hinz and H. Koch. The Linear Elamite script however, one of the scripts used to write the Elamite language circa 2000 BC, has remained elusive until recently.
The approaches taken to decipher this language from the various scripts in which it is written resembles similar efforts to crack early Minoan and Greek written works.
Some recent developments in understanding its script came up in a review of two newly released books on the history of writing.
Being able to read a script is not the same as understanding a language. Even if the new hypothesis does find general acceptance, significant gaps will remain in our knowledge of Elamite grammar and vocabulary. It doesn’t help that Elamite is “isolated,” that is, unrelated to any other known tongue. All the same, there is now reasonable hope of translating what survives of the records these adventurous ancient traders left of their world.Deciphering unknown languages often depends on the fact that the same language can be written in multiple scripts (as with Elamite, and later Turkish or Malay), and the same script can be used to write multiple languages (as with cuneiform, and later the Latin and Cyrillic alphabets).
A paper published in 2022 claims to have almost fully deciphered the Linear Elamite script. The paper and its abstract are as follows:
Linear Elamite writing was used in southern Iran in the late 3rd/early 2nd millennium BCE (ca. 2300–1880 BCE). First discovered during the French excavations at Susa from 1903 onwards, it has so far resisted decipherment.
The publication of eight inscribed silver beakers in 2018 provided the materials and the starting point for a new attempt; its results are presented in this paper.
A full description and analysis of Linear Elamite of writing, employed for recording the Elamite language, is given here for the first time, together with a discussion of Elamite phonology and the biscriptualism that characterizes this language in its earliest documented phase.