I use Roundup on weeds I can't kill with hoeing and uprooting. I see now from Jennifer's link that it is more persistent in soil than I thought. BUT it does still break down
the claim that is not rapidly taken up by nearby roots may be true, because I observe that the only plants that die are those whose leaves I sprayed.
(Please don't yell at me because I don't hate Roundup! It is better than some other herbicides.)
I think Roundup gets a worse rep than necessary, partly because it came from Monsanto, partly because it is part of the "Roundup-ready" series of crop seeds, and partly because there are so many REALLY hideous persistent herbicides.
I understand and mostly agree with the indignation about the commercial practice of "kill everything in sight and then plant patented seeds". But as with medication, "the dose makes the poison", and many things are terrible when used without moderation, but manageable when used judiciously.
Your mileage may vary.
The smartest thing has been said by several people: don't use a chemical toxin if another method works. One lady's comment about how to kill weeds was: "ON YOUR KNEES, like God intended!" That, I can't do because of my legs, but I do hoe, rake, dig and pull awkwardly but repeatedly. I dig up the soil with a mattock and screen out roots (but not weed seeds). I can cover with tarps or paving stones. I have plans to buy a "weed flamethrower".
But when those don't work, and a perennial bed is disappearing into some nasty weed, I will use Roundup.