For a ~50-year-old program, Emacs’s support for multilingual input — and really, it’s all-round flexibility — continually amazes me! For myself I prefer my own custom keyboard layout [0], because it works outside Emacs too, but I’d happily use Emacs’s own input methods if that would be sufficient.
(In fairness, I have found one weak spot, namely font support… I’ve used ‘unicode-fonts’ [1] with some success, but reportedly it doesn’t work with the latest Emacs. Ah well, it’s at least fairly rare that this becomes a problem in practice.)
Emacs is a bit crazy about it... it has its own set of input modes which include modes you may not be familiar with. You can use various IMEs that plug directly into Emacs rather than relying on a systemwide IME (which was neat back when systemwide IMEs didn't work well), and there are systems like RFC 1345 (type &e' for é, &e* for ε, &12 for ½, etc), or TeX (type \'e for é, \varepsilon for ε, \frac12 for ½, etc).
So many people have their own preferences for how to type these characters, write an input method for Emacs, and get it included.
(In fairness, I have found one weak spot, namely font support… I’ve used ‘unicode-fonts’ [1] with some success, but reportedly it doesn’t work with the latest Emacs. Ah well, it’s at least fairly rare that this becomes a problem in practice.)
[0] https://github.com/bradrn/Conkey
[1] https://github.com/rolandwalker/unicode-fonts