00s -- нулевые, 10s -- десятые, 20s -- двадцатые, 30s -- тридцатые, ... , 80s -- восьмидесятые etc. using respective plural ordinal numbers.

семидесятые, восьмидесятые, и т.д. 00's and 10's are a problem:) Sometimes I say 'двухтысячные' (meaning 00s), but this is ambiguous. Some jokingly say 'нулевые' but it sounds like a joke). I avoid 2010s. It seems it is personal ad hoc inventions. In books they use 1900е, 1910-е etc. sometimes.

the Seventies/Eighties/Nineties = Семидесятые/Восьмидесятые/Девяностые 2000's = Двухтысячные as for the 2010's, 2020's, I'm afraid nobody uses these forms for now. Therefore, there is no answer. Or, as it has been mentioned earlier, it will be an invention. If I have to say "in the 2010s", I would say "В две тысячи десятых годах".

Thank you very much! :)

2000's = начало двухтысячных, нулевые 2010's & 2020's = there is no colloquial way as we are still in the middle of 2010's, so we mainly refer to a precise year, not to a decade. I suppose when we pass the 2010th year, we'll use the similar expression we use for 1910's... десятые двадцать первого века, десятые годы двадцать первого столетия.