The Tipiṭaka, or Pāḷi Canon, was first written down at the Fourth Buddhist Council in 29 B.C.E. at the Aluvihāre Rock Temple in Sri Lanka. For those ~450 years from the time of the passing of the Buddha (parinibbāna), the teachings were memorised and passed down orally. Scholars believe that since that first written record, the Tipiṭaka has pretty much been “locked down”, with minor changes and additions coming in afterwards.
Despite the 2,000 year written record, and now digital libraries off and online, that tradition of memorisation continues on to today, but perhaps not as systematically and widescale. I often marvel at the prodigious memories of Burmese monks, almost all of whom can recite the entire paṭimokkha, eleven paritta suttas, the Dhammapada (if not the whole thing, then at least large swaths thereof), and many long suttas, i.e, Dhammacakkappavattana Sutta, Anattalakkhaṇa Sutta, Mahāsatipaṭṭhāna Sutta, etc., not to mention lots of ceremonial stuff. I once asked one of my teachers how many suttas he could chant, and his reply was, “Not much. Maybe 50 or so”, his tone giving the impression that he felt he was a bit of a slacker!
Then there are those select monks who make it their practice to memorise the entire Tipiṭaka, to be tested on it, then to teach others with that encyclopedic knowledge. The first monk to receive the title Tipiṭakadhāra, or Guardian of the Tipiṭaka, was Mingun Sayadaw, U Vicittasārābhivaṁsa, at the Sixth Buddhist Council held from 1954-56 in Myanmar, who correctly answered all the questions posed by Mahasi Sayadaw based on the entire content of the Canon. Since then, there have been another twelve, eight of whom are pictured below.