Maya script is a very rich and complicated script, and the colonizing Spaniards did an outstanding job of eradicating it. For example, they managed to destroy all but four books written in Maya script.
Fortunately, many carved examples of Mayan writing were not so easily destroyed. In addition, notes taken by the very man who ordered the destruction of the books were a hugely important clue in relearning how to read Maya script.
Maya script was logosyllabic, with many logographic symbols in addition to a full syllabary. To complicate matters, some glyphs could represent either a logogram or a syllable. To make it even harder to decipher, each syllable could have several different glyphs for it (sort of like how the first sound in “fan” is spelled “f” in some words and “ph” in other words).
In addition, the syllabary was made up of consonant-vowel (CV) syllables like “ka” and “lo”, yet the language had syllables that were actually consonant-vowel-consonant (CVC), like the English “cat”. They had relatively complicated rules for how to combine two CVs to make a CVC (i.e. how to show that a vowel should not be pronounced).
That’s not all: for multi-syllabic words, they smashed glyphs for syllables together into one blocky character.
To make it even harder to decipher, the reading order wasn’t left-to-right, or right-to-left, or top-to-bottom, or even bottom-to-top, but rather in a vertical sawtooth pattern! You start at the top left, then go right one, down and left, right, down and left, right, etc. until you get to the bottom. You then go to the top of the third column and start over.
But wait, it gets worse: there were several different languages that were all written in Maya script.
It’s understandable why nobody made any headway in deciphering the script until 1952. It’s amazing it got deciphered at all.
Links: Wikipedia, Omniglot, and an excellent article at Ancient Scripts. Glyph drawn by Zykasaa.