Generally, do the general-purpose mutual funds from the big brokers like Fidelity, Vanguard, Schwab include international companies, or is it mostly US companies?

I'm interested in investing in other countries, but I don't know if it's strictly necessary to choose a fund that says "European" or "International" on the tin as I'd like a mix. Is there an advantage or tax issue with investing in a European broker? Any recommendations there?

Thanks, folks.