That's where we disagree: I think we understand them quite well. Well enough that there's no open questions leading us to believe there must be something else. Fields alone describe all of modern physics. As such, there's no indication that there's something more fundamental than fields.

Contrast this with atoms: there are things atoms alone cannot explain, like the Zeeman and Stark effects. There must be something more fundamental going on. (Spoiler: It's fields.)