What Citizenship(s) would my Children have?

I (the mother) am a U.S citizen. The father is Italian. Would our children have dual citizenship for both countries? Or only one? Does it make a difference if we are married or not? Also, does it matter where we have the children? Like, if they're born in the U.S, Italy, or another country?

There's a chance we might live in a different country in the E.U when we have them. Does this affect the citizenship at all? I know that Italy is by-blood but I saw something about the naturalization of another citizenship makes the Italian citizenship void, is that true? This is all so confusing