To view current and completed downloads; tap the magazine page to reveal the extended magazine control features. Then tap the downward-pointing arrow in a circle to reveal the Downloads pane:

This pane will allow you to view current and completed downloaded magazines. You can also stop and delete current downloads, as well as deleted already downloaded magazines by tapping the “X” on the file you want to affect.

NOTE: Downloads in progress will only continue while an app is running. Any in-progress downloads will stop when an app quits. Pending downloads will resume as soon as the app is restarted.