He has 2 or 3 distinct 'periods' that can be roughly delineated by the label he was signed with at the time. His Asylum years go from about '73 to '80, mostly made up of his scat & barroom ballad stuff; When he signed with Island from about '83 to '98 he got very experimental; howl & growl, German cabaret & banging pots, etc and a lot of his old fan base was turned off by it, but I think much of it is brilliant (with one exception*.) In '99 he came out with his first on the Anti label, Mule Variations, which was the first Waits album I ever heard & bought...it was love at first listen. I've got just about everything he's put out, as well as a few bootlegs. His entire oeuvre takes up a full 1/5 of my old-ass Ipod Mini.
As for how to quantify the newer material...I'm tempted to say its a hybrid of his Asylum & Island stuff but that's way too simplistic...I'm sure Gagh could wax far more eloquently about it.
*The Black Rider, which for the life of me, I just cannot get into.