Trimming your iPhone's podcast library prevents episodes or shows from filling up your iPhone's hard drive. While unsubscribing keeps new episodes from being downloaded, you have to manually remove the old ones from your iPhone. You can remove entire podcasts or individual episodes, giving you control over how much content you want to delete.
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To delete an individual episode, open the Podcasts app and tap the icon for the desired show. Find the episode you want to delete in the list and swipe left across the episode's title to summon the Delete button. A quick tap of this button deletes the episode from your iPhone.
To delete an entire podcast, open the Podcasts app and drag down on the top of the screen to reveal the Search field and Edit button. Tap the "Edit" button and tap the "X" box in the upper left corner of the desired podcast to delete it. If you're using List View instead of Icon View, you'll see red circles with dashes through them appear next to each podcast's heading. Tap a red circle and then tap the "Delete" button that appears to delete the podcast.
You can also manage all of your podcasts from iTunes, deleting or syncing new ones as necessary. Make it a habit to regularly prune your podcast list of unwanted episodes or shows, especially if you listen to a lot of shows. Only keep the episodes you're going to listen to more than once; otherwise delete them to free space for newer episodes. If there are episodes you really want to keep, consider archiving them on your computer to save your iPhone's storage space.