It's unclear to me how to acquire and manage podcasts in Apple's Podcasts app, especially how the syncing of podcasts using iTunes works with that app. As others have reported elsewhere, the relationship between these two methods of subscribing to and tracking the "reading" of podcasts can be confusing.
How does the management of podcasts in iTunes relate to the management in the Podcast app? How does the management on one iOS device relate to the management on another?