When you click "Borrow" on a book summary page in BC's Overdrive...

...the book is stored in your bookshelf:

At this stage, you can return it within your Overdrive account. However, if you download the book for use on a handheld device (such as an ePub or Kindle eBook), the "return title" button will disappear, and you will need to return the book through the app you are using on your handheld device, such as Kindle Reader or iBooks. Another option is to simply wait until the loan period expires, when the title will automatically be returned.
Please be aware that books checked out through Overdrive will not appear in your Catalog account active loans list. Books expire, so there are no late fees.