I cannot see any spellchecker and do not know how to install one. I am interested in English and Greek.
https://extensions.libreoffice.org/@@search?SearchableText=greek+dictionary
https://extensions.libreoffice.org/@@search?SearchableText=english+dictionary
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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.