Amazon's Android Appstore held great promise when it was announced, but the reality has often proven annoying to use. A big part of that was the terrible Appstore app that was used to install purchased content on a device. Today things are getting better in that department. The Amazon Appstore client has jumped from v5 to v7 and has gotten a complete UI overhaul in the process.
The new UI is still recognizable as Amazon, but it looks more like the updated Kindle Fire tablets, and less like something designed explicitly to taunt you. The scrolling is vastly improved and there's no more legacy menu button (yay). The interface is still a bit confused by Android UI standards – there's a menu overflow button on the left that opens a navigation drawer, for example. There are still a few spots of lag too, like scrolling in the navigation pane.
You can grab the new version of the Appstore directly from Amazon's site, but devices might not show the update when you check from inside the app at this time. There's a download link at the bottom just in case. There are also some screens from the old app below for comparison.
[Amazon – Thanks, TheManii and Victor Lee]