Direct compost: Dig a trench, put in chopped greens, fill trench with soil.

Or give with a friend/neighbor who has a pile.

Or toss in trash.

I like the direct compost idea. Do I dig up the trench later to get the compost or just bury it near the place I will plant beans next year and leave it?

I did like you said, ran over them with the mower, dug a trench and buried what I could. The rest of them, I buried / dug over with the raised bed soil and wood chip mulch and made a big sloppy mess. Don't know if this was bad- ie, wrong time of year, wrong method, etc. I did this with green vines because when I let things dry out they make a large amount of plant dust that irritates my asthma.

That will work.

concur. I trench everything, squash,tomatoes, beans, cabbage stems. usually in a single trench for practical reasons.

Trench composting ... bury it and leave it.

It works well if you can alternate the trench locations ... year 1 you are filling one up in an unplanted area. The next year, you plant next to the trench and leave another spot bare. Dig the trench and leave it open, cover each batch of stuff as you add it and pack it down.

Or trench compost around, between and behind the plants in an established border to add some nutrients.

Yes, alternate. I also add rotten branches and leaves. Good fungal population together with earthworms.Plants roots seek rotten wood, and happily sink into it.

I never head of leaving the base and roots of a plant in the soil. What are the benefits? Who recommended it?

so long as the plant dies, it will compost in place. If you leave it in place, but rotate crops, it will be fine.

Ma Nature recommends putting the plants that grew there back into the soil since she does that every year.

I read somewhere on this site to clip the plants at ground level and leave roots in place to 'return the nitrogen to the soil'. I figure it is just another form of trench composting or composting in place.

I could not leave them in place to die and rot, they were attatched to a rather large piece of homemade trellis and it would have been an eyesore in my tiny yard to let it remain. I did as one poster suggested- ran over the vines with a lawn mower and buried some, dug some into the garden bed.

The theory seems to be simple. Cut the roots and they will rot, leaving broken down organic materials and water channels down into the depths, whatever they are. Pull them out and you are pulling out organic material.

It may matter, but not too much, and mostly to those who don't like to dig around. I dig, but as little as possible, and find it very convenient to lop things off at ground level (especially things that are stout like sunflowers) that would cause some turmoil in their pulling to adjacent plants still living.

Who recommended it?

How about Mother Nature? That's how she handles it. Tops die back seasonally and the plant roots remain in place. They decompose in time, adding back organic matter (as will the tops if left also, or trenched, as suggested above).

We tend to be obsessive about garden clean-up, removing everything after harvest or when annuals/perennials die back in winter. But leaving plants in place, provided there are no disease issues present, removes or reduces the need for the constant additions of organic matter that healthy gardens and soil require.

It's nothing I would do. Sounds like an invitation to trouble. Fungus, disease and/ or bug problems. Let us know how it works out for you.

fungus are your friends, specifically they are friends of your plants. I would never plant a tree without making sure its roots are in touch with fungi.

Beans fix N from the air so best to leave those roots and compost the vines (in the garden or bin). I don't leave tomato, potato, or pepper plants in the garden b/c of disease. Plus pepper stems are too woody to break down over the winter. I pull them and trash them, along with any cucurbits with PM, DM, or SVB.

I'm wondering though, if beans have rust, is it safe to till them in, should I compost them instead, or throw them out too?

LOL!! Gardeners have been doing this for eons. It is the principle behind cover crops, for heaven's sake. It is just another way of composting. Do you think farmers, after harvesting their corn and cutting down the stalks, go out and pull all the roots up? Heck no! They till them in to the soil to add back organic matter.

In our, often, monoculture gardens putting diseased plant tissue back into the soil may be somewhat problematic, but if one follows common organic practices that would be minimized. Ma Nature does not remove diseased plant tissue from her gardens, they are there and often are kept somewhat under control by 1) diversity, and 2) bio controls.
Even those that advise people on "conventional" gardening practices advise them to practice crop rotation for plant disease control and that (plant disease) is a larger concern in "conventional" gardens.

I'm glad you had a laugh at my expense. The farmers tilled it in. So they didn't just leave it in the ground to rot where it was planted. I wouldn't do it here with all of the heat and humidity.