Are characters limited to 20th level in 5e?
Context: the last version I played was AD&D (ie. 1e) where characters could (technically) progress to unlimited levels. Looking at the 5e PHB I get a sense that 20th level is now a concrete ceiling in terms of character level, and no progression beyond that is possible -- but I can't find it explicitly stated anywhere. Is this the case?
(NB. I'd have no objection to a Lvl20 limit, but I'd like to know for definite, since of course it has a major impact on how one plans a multi-class character).
Currently the rules provide no provision for a character to progress beyond level 20.
With that said, they don't explicitly ban it, either, and as you've noticed, it would be simple to continue using a multiclass. The only things you would need to come up with houserules for would be proficiency, experience requirements, and multiclass spell slots.
Personally, I would rule that proficiency progresses according to the proficiency by CR table on page 8 of the Monster Manual. Multiclass spell slots could continue to gain 1 per level in the existing pattern (I can see it but I can't explain it) and experience requirements could continue to rise by 10000 every 2 levels.
Updated with the release of the DMG: The DMG includes suggestions for character advancement past the level 20 mark. This is the Epic Boons section on pages 231. The gist of it is that for every 30000 XP a character earns past level 20, they receive an epic boon. The list of Epic Boons is on page 232; they are essentially like feats, but considerably more powerful.
Mainly I wondered if I'd missed something in the rules that talked about levels above 20th, or specifically stated that such a thing is impossible. Seems I didn’t; it's just been left ambiguous. My personal view is that I'd probably keep to the 20 level limit, with the limitations that it inherently places upon multi class characters (no more than 20 class levels in total). That seems in keeping with the tone of the 5e rules, which are clearly written with a view to characters never becoming zany powerful.