Libby is a reading application by OverDrive that allows you to borrow, read and return books and magazines from your library. They had an OverDrive app itself, but seem to be migrating those users over to this app, which is designed exclusively for the reading experience.
I use the Libby app on my Android phone and tablet. But helpfully, the same can be accessed in any browser at libbyapp.com.
The interface is modern, clean and simple. Once my library card is added, I can search for ebooks and magazines. The app allows me to borrow them and the items I have borrowed are displayed on the shelf. It also shows me when they are due and allows me to return them back. By going to the shelf, I can click and read any of my borrowed items.
Magazines open by default in image mode - where you read the print magazine page images. In print magazine mode, it shows a table of contents at the bottom for quick navigation. It also supports placing bookmarks on the pages. The killer feature of this app, is that it allows switching to article view (see icon at bottom) which renders the text versions of the article, just like in an ebook reader.
The app also supports borrowing and listening to audiobooks. I have not tried this feature yet since I do not listen to audiobooks.