I use boiling water to kill any stubborn weeds
around the yard (like the curly dock). It works surprisingly well, you just have to be a little patient (a given if you garden without chemicals) because if you just dump the whole pot on it will run off and kill something else nearby,I pour it on a cup at a time so the heat soaks down and gets the root.
I especially like to use my leftover water from cooking veggies because it is full of vitamins and minerals.
I think the vinegar is also a good.
And if you want to stop them before they get out of hand the best thing is to lay down cardboard or newspaper(not the colored stuff) because it also is beneficial after it decomposes.