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Assuming you have an "annual"Assuming you have an "annual" sunflower: After the big sunflower heads droop down, the seeds will dry out and you can harvest them or watch the wildlife enjoy them. Once it's done, you can pull the plant if you wish. For perennials (which come back), you'd cut back the foliage after frost kills it back.

2015 Special Edition Garden GuideCooking Fresh with The Old Farmer's AlmanacThe Almanac Monthly Digital MagazineWhat the heck is a Garden Hod?