In the early game, spells faced tremendous limitations on their use. You had to be standing upright, with both hands free, not moving, concentrating, with all the components at hand, speak loudly enough to be clearly heard, be able to hear what you were saying (deafness carried a chance of spell failure), and if you cast in melee, you were (though there were two different, contradictory rules for it), likely to be attacked in the act of casting, and, if hit, the spell failed and the memory of it was lost. Spells that required concentration had most the same requirements as concentration when casting, and said concentration was automatically broken by any damage, at all (and potentially other things as well).
3e softened all that: you only needed one hand and the ability to speak and feats could eliminate those requirements, could be crouching behind cover or even prone, and/or moving including riding a fast-moving mount, material components were consolidated into the spell component pouch, concentration allowed a check that you could buff up the wazoo, you could also use concentration to avoid an AoO, but being hit by said AoO only caused you to lose the spell if you failed another concentration check, a concentration check could even allow you to cast while grappled. (3e also made save DCs scale with slot level, while simultaneously making some saves worse for most characters, but that's not strictly-speaking a relaxed limitation, nor would more slots or metamagic or liberal item creation be).
4e further simplified and softened limitations on casting, let's say 'net' - for instance, AoOs could no longer be avoided with a concentration check, which would seem like tightening a restriction, but, AoOs were only provoked by Range & Area spells, which were no different, in that, from all other range/area attacks. So it was a limitation, but not only on spells, nor on all spells. Concentration checks were no longer required, if you were hit while casting your spells still went off if you were still able (alive, not stunned or anything), again, just like any other attack. Concentration as a duration was changed to 'Sustain,' which required an action, usually minor, sometimes even Standard. You still needed just one hand & the ability to speak, you could be under any condition that didn't actually prevent you from taking the required action type and still cast. Components were further consolidated into implements. Rituals were broken out and no longer used the same resource pool as attacks. (Of course, there were far fewer slots, and they were locked-in, even wizards, who could prepare, had very limited selection and couldn't take the same spell 'twice,' and spells were far less powerful. But those are less strictly limitations.)
5e further softened the limitations on casting, though it did increase the overall complexity some: You still need only one hand, can consolidate material components down to a 'focus,' and can cast in any circumstance or condition that doesn't deny you the required action type. Spells provoke no AoO. Sustain was returned to Concentration, required only for a select few spells, took no action at all, and could be maintained with a check even when damaged. (And of course, spells powered up and slots far more numerous - and all casters are freak'n spontaneous, which is huge.)
