What happens to the top layer of dirt in a dig?

Over in the old world, I recall that Medieval archaeologists would complain that people looking for earlier sites would shovel off the layers that were of interest to them. Then Post-medievalists started yelling at the mediavalists for doing the same thing to the layers that they were interested in!

That sort of thing can be dangerous. I heard an almost apocryphal tale of a research project in the Northeast where, after preliminary testing, the archaeologists brought in heavy equipment to remove later deposits than the period that they were interested in. Only to discover when they got out into the field--with paying field school students--that they had pretty much removed the entire site.