I do part time farming in dry land. Cultivation is the key for keeping soil moisture, so this is the tool that I almost always use to eliminate weeds. I do not use herbicides, but every rule has an exception.
Vast areas in La Mancha were a monoculture of vineyards years ago. After uprooting them, some plants were not completely removed and remain in the fields. Lazy people leave them there, so they remain as perennial weeds. When I prepare a field to set up an almond orchard, I dig those vines out and keep the soil clear. But last winter I bought a mature orchard full of those tricky vines. It was not practical to dig deep because the soil was hard and I did not wanted to damage the almond roots.
I looked for herbicides that may be effective to wipe out perennial weeds. I learned that glyphosate is systemic. There are plenty of cheap formulations in the market. I used 36% Glyphosate (isopropylamine salt) at the lowest recommended dose. I did that in early June, when vines are big enough and still growing. This is important, because glyphosate mode of action requires young tissues. I soaked only the target weeds using a manual sprayer. 20 hours later the product was washed by the rain. It took two months to really appreciate how effective glyphosate is. The tricky vines deteriorated slowly, but finally most of them die.
These particular perennial weeds are under control with just one application of glyphosate. I marble at the effectiveness of this herbicide, which rapidly deteriorates in the soil and does not harm the plants that are not sprayed. Using it has been a worth doing exception.