The 2020 trip to Argentina was our first example of test requirements for international travel.
If we haven't sent results to AstroTrails before we leave Dec. 10, we will not be accepted on the tour when we get to Buenos Aires. They specifically said that an electronic result shown upon arrival will not be accepted.
Two people from Scotland did not get their PCR test results in time and were not allowed to go on the trip.
So rule #1: Do not depend on getting tested at the airport like the LaGuardia $#!%show James described. And do do not accept anecdotal stories about people getting their PCR results back in one day at a pharmacy or some other free site. You need to find a place that guarantees 10-12 hour PCR test turnaround. Those tests cost $180 in Dec. 2020. This year we found a place that charges $75 but then bills your insurance for the rest.
Chile required preclearance of vaccine information. It needed to be submitted online, and if approved you got an online Mobility Pass in about 3 weeks. We furthermore had to submit the fast PCR results online and get an acknowledgement form back from Chile on that. So rule #2: Don't assume showing a vaccine record at your departure airport or upon landing is sufficient. We were not checking in for our flight at LAX without showing the above documentation plus proof of medical insurance covering COVID and good in Chile.
The travel agent TEI gave us a detailed heads-up about Chile's requirements. Nonetheless there were a few people who didn't pay attention and needed some last minute intervention from TEI to get into Chile.
I doubt the Eurozone will make us jump through as many hoops as Chile did, but I'd recommend thorough investigation in advance for each country just to be safe.
I've generally been resistant to using my smartphone as a data repository. But now I have a Notes file where I have pictures of passport, driver's license, medical insurance cards and COVID vaccination record. I put both my and Liz' Chile Mobility passes in there. We were often requested to show the Mobility Passes to enter restaurants and for some of the domestic flights. L.A. County requires proof of vaccination at most sports and concert venues (usually they check) and restaurants (maybe 10% check). So I would definitely have that info on my phone, preferably in electronic form with a QR code as California and Chile use. I realize there are some US states that do not provide such forms so you might have to use photos of your CDC card(s).
We were unable to get a COVID test in Puerto Varas, so had to drive in and out of Puerto Montt to a clinic there in rush hour traffic that would do L.A. proud.
For returning to the US, the negative test needs to be no earlier than the calendar day before arrival in the US. The good news is that the US does not require PCR. You can get the cheaper antigen test where results are routinely available in half an hour. I found a clinic in Puerto Varas online before we went to Chile. We showed up at noon, were told to request an appointment online, then learned at 2PM none were available that day. So Liz had to call around and find the place in Puerto Montt. So rule #3: So do the research in advance where you can get an antigen test on the day you need it to come home and then make an appointment.