Of course, normally they would be excavating a mediaeval or Roman site, but I remember seeing an episode where they were digging up a crashed WW2 B-17. That expanded my idea of what archaeology could be.
In series four, there was an episode in the US¹ that I found quite jarring with the discussion of prehistory finds only a few hundred years old. Obviously, the term has a different meaning given the context, but it still sticks in my mind to this day.
It goes from 124,000BC (ok, seashells) to the 1300s (old pottery, cooking utensils), to 2005 (flippo disks, ID cards, probably some still functioning Nokia phones.) You can browse it here: https://belowthesurface.amsterdam/en
On the other hand, just because an investigation of a somewhat recent event is digging through material doesn't make it archaeology, but I guess that's partially distinguished based on motivations? (e.g. accident/crime investigations etc)
EDIT: younger example: https://www.archaeology.org/news/8291-191213-south-carolina-... "Archaeologists are investigating a possible Vietnam War–era military training site at Fort Jackson, an initial entry training center for the U.S. Army in South Carolina, according to an ABC News report." - I guess discarded beer cans could be useful dating something like this
https://www.worldcat.org/title/archaeology-of-the-cold-war/o...