Go back in time far enough and there were at least 3 ways to measure bitterness, it has for the last 10-15 years been unified, most people call it IBU (international bitterness unit) it is generally regarded as being mg/L of iso-alpha acids / L of finished beer.
American literature often calls it a BU (bitterness Unit) (US comes with a built in reluctance acknowledge there is a rest of the world - some times the poms aren't far behind)
Some of the oldest methods involved a taste test which were very non linear as well as being fairly unreproducible (best guess method). The best of the modern methods uses HPLC, very accurate and repeatable.
Mark