Linear Elamite petered out after a few hundred years, ignored in favour of more prestigious languages/writing systems like Babylonian (which was an organic descendant of Akkadian in both language and script). When the Elamite language reappeared after a few hundred more years, it was written in a modified version of the Akkadian cuneiform. The number of signs varied over time, but there were never more than about 130 signs in use at any one time.
More of Elamite cuneiform has been deciphered than of Linear Elamite, in part because of similarities to Akkadian cuneiform, but also because of some very well preserved, long texts in multiple languages. The most famous example is some big honkin’ inscriptions at Behistun, Iran that are 100m up a cliff (i.e. relatively safe from vandals) telling of Darius the Great’s exploits. These inscriptions were not only important for deciphering Elamite cuneiform, but also for deciphering Old Persian cuneiform.
The upright wedge glyph at the beginning of this post is a “determinative” in Elamite cuneiform. Most languages that were heavily logographic also had phonetic aspects that make it frequently ambiguous. A glyph might represent a word/idea/thing, or it might represent a sound. (For example, you can imagine a writing system for the English language where a drawing of a bee might mean either the sound “B” or the little insect that buzzes around.) To give the reader some clues about the adjacent word, many heavily logographic languages had additional, unpronounced symbols called determinatives which classified the adjacent word.
The determinative glyph at the beginning of this post is for people: proper names, names for classes of people (like “king”), relatives, and some pronouns. Sumerian cuneiform also had determinatives for such things as “trees and things made of wood”, “rivers or canals”, and “buildings or temples”. Egyptian hieroglphics had determinatives for almost everything, like “vine, fruit, or garden”, “fire, heat, or cook”, or even “bodily discharges”.
Thus, to read languages like Elamite, you needed to know a very large number of logograms, syllables, and determinatives, some of which were ambiguous. You had to — on the fly — figure out whether to pronounce the characters or not, and if a symbol represented a word or sound. I will never complain about English spelling again.