Some of the new elements are:
A new Shuffle Play button
Previously, this was just a simple "shuffle play" button but the new icon is now one click of a button.
Easy to use Action Rows
The primary Spotify user actions - like, play, and download for Premium users - are now grouped in a row which is more adaptive and responsive according to screen size.
New Track Rows with album art
The update will also now show album arts in all views (except Album view), making it easier to navigate through familiar songs.
Do you use Spotify for music streaming, and/or for podcasts? Chime in.