The Greeks had no concept of an arch as we know it. The Greek temple design is incredibly elegant, and one of the most copied building designs to this day, but it amounts to piling one thing directly on top of another.
They did have an arc they could build, of a type called a corbel arch. Here's an example:
This is the famous Lion Gate at Mycenae. I took this picture myself, many years ago. The stones above the lintel have been placed to overlap a bit, one above another, so that you get the illusion of an arch in negative. The stones would stay there even if the relief of two lions didn't fill the gap. By classical times, even the corbel arch had pretty much disappeared from Greek designs.
It remained to the Romans to come up with what we call the Roman Arch. I've rarely seen a better example of a Roman arch than this fine example:
As you can see, the whole thing would collapse in an instant if gravity wasn't pulling down on every block. Or in this case, on every computer monitor. It relies on shaping every block exactly for its position. The topmost block (monitor) is hugely important and is called the keystone. It's really very clever. The downside is nothing can stay up until everything's in place. So they'd build wooden supports beneath and then knock them away after the keystone was in.
The one thing both Greek and Roman architecture have in common is they both use gravity as glue.