What spellcheckers are available and how do I get them? Is there one for Greek?

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Also read this tutorial.

For linux users, execute sudo apt install hunspell-xx. At least for Libreoffice from V5 on this is the way to do it. XX stands for language code. I came across this after worrying that Dutch is not available as extension ;-) Hunspell is a generic spellchecker that can be used with other programs as well.

Addition: Hyphenation can be enable by doing sudo apt install hyphen-xx.

For linux users, execute sudo apt install hunspell-xx.

Nonsense. It is for users of Debian and its derivatives only. Other distros have other means (such as zypper in openSUSE).

Do not give advise when you do not know the matter.

I complain about this unfriendly comment. That's not according to common commenting practice. However, that does not affect the issue itself. Here you're correct. Now I realise that I had no distro differences in mind at the time of writing.