Okay sorry for the stark title, but I've had yellowy/white discharge for a few months now and it comes to the point that my underpants are often wet. What could this be?

You didn't say what age you are, so I'm guessing that you are quite young. If so, this discharge is normal, and is the reason you see so many ads for panty liners. You will find it varies through the month, sometimes it's yellow/white, other times it's clear, like egg white, and sometimes there is very little.

If it's itchy, or has a nasty smell (as opposed to a normal female smell) then you may need to ask a doctor or Well Woman clinic.

I had this problem all the time when I had an IUD. Apperently the little retrieval wire-string was an irritant. Removing it ended it.
If you are doing activities where you sweat more, that can affect you 'down there' too.
If there is no itching or weird smell or other signs of infection, buy some little pantiliners and don't worry about it. The stores sure sell enough of them, even ones that fit a thong, so you are not the only gal with that problem.