[09/08/2021 @ 01:08 PM] Price drop to $284-$579. Was $362-$658. Note that Italy, Spain, Netherlands, Belgium, Sweden, and Norway have increased travel restrictions.
[09/09/2021 @ 01:27 PM] Greece plans to continue to allow US tourists until at least the end of their Tourist Season, per Tourism Minister.
[09/17/2021 @ 11:12 AM] Netherlands drops quarantine requirement for vaccinated tourists.
Star Alliance, Oneworld, and SkyTeam carriers have flights to Europe on sale with a price range between $284-$579. Flight dates are mostly between September and April of next year. Smaller airports will have more stops or worse routing than major airports. Prices to Europe have been low for the past two weeks so far.
Expect prices to shift around +/- 10% as the deal ages. Competing airlines will match, un-match, and move prices around when they have sales to the same region. Those price changes can happen multiple times a day.
Be sure to research your destination before finalizing any travel plans. While most EU member states have not made any changes to travel restrictions, several have (see links in Timestamp).