The first version of D&D that I played - Basic - instructed players to roll 3d6 for each stat and assign the number to that stat. I believe these are the rules for OD&D as well.
In AD&D the "standard" method was to roll 4d6, ignoring the lowest dice, five times and then pick which stat you assigned each number to. The same system was used in 2nd, 3rd and 3.5 editions.
4th and 5th both use a standard set of scores, assigned to stats as the player wishes.
In all editions there were variations to the "recommended" rules, most notably the plethora of systems introduced in Unearth Arcana. For the purposes of these questions, we'll bypass those and stick with the typical versions.
Are my recollections of the different systems correct? Can anyone explain the drivers that lead to the changes between editions? I am particularly interested in the switch from 3d6 to 4d6, dropping the lowest.