Are cover crops in grain fields harvested?

Question by farmgirl: Are cover crops in grain fields harvested?
This may be a silly question but I was wondering, when farmers plant a cover crop such as buckwheat in their grain fields do they harvest the buckwheat grains along with the main grain or is it just turned into green manure?
I understand that they are used for weed control, but I was wondering what happens to them after the grain plants are harvested?

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