I am aware that the translation of Egyptian hieroglyphs were helped because of the discovery the Rosetta Stone which has the well-known Greek writing on it, but how did archaeologists and historians deciphered the cuneiform and Sumerian language?
As far as I know cuneiform writing was also used by the Persians, the Babylonians, the Assyrians, and other civilizations, and that some languages using the script has surviving members from the same family e.g. Akkadian is in the Semitic language family, but how did we managed to piece together information to figure out the Sumerian language, which (IIRC) is a language isolate and doesn’t have any living relatives?
Not to preclude further answers, but I wrote about this in When did the modern understanding of the history of Bronze Age Mesopotamia develop?