Many North Americans are puzzled by what happens with their encounters with officials on landing in Europe, what is sometimes lumped together by them as "customs".
The three activities after you get out of the jetway or bus and make the long walk are Immigration, baggage collection and finally Customs.
Immigration tends to be the slowest. That is because the Immigration officials are interested in WHO you are, when they decide if you have what they need in terms of answering their questions, checking your identity, checking and stamping your passport, and if they don't like the first bunch of answers arranging for secondary questioning. If you get behind somebody who causes questions it will hold you up. If you get behind several of those, everybody in the line just waits their turn.
On the other hand, sometimes you get somebody who asks few questions, everybody has their passport open to the correct page, and the line fair hums along.
Then it is to the baggage carrousel where if Immigration isn't on greased lightning you bag will be waiting for you, gently circulating.
Then to Customs. They care only about WHAT you have with you that you are bringing into the country. These are the guys (and ladies) in the US who take everything out of your cases and ask lots of embarrassing questions about the fish heads you are bringing back.
In Europe (I haven't done Athens but I am sure it is like the rest of EU land) generally Customs is a non-event. You will be presented with three channels, or streams or doors to exit by. The rotating knives are behind the middle door, usually, the booby prize is often behind door number one, and the car and the boat are behind door number three, usually.
Oh wait - wrong show!!! oops sorry.
Back to Customs. The three channels usually, for an EU country, are "Nothing to Declare", "Something to Declare", or "European Union". They are often, but not always, identified by colour - Green for Nothing to Declare, Red for Something to Declare, and Blue for EU.
Usually that part is just a walk through - but even though you can't see the inspectors they are there watching, and can pull people out of the green channel - and then you are through the frosted glass doors and into GREECE!!!