When Outlook.com finally replaced Hotmail, a (re-skinned) Hotmail was now the Outlook.com app. However, for those that complained about a simple re-skin from the old Hotmail app, you'll be stopped in your tracks with yesterday's update.
Yesterday's update delivers a whole UI change in the app, which looks a lot more like the web version of Outlook.com on the desktop. It also resembles the Outlook.com mobile app for Windows Phone:
This look should feel a lot similar to the Outlook.com interface, and the Microsoft online services in general. Clicking the 3 stacked dots shows the menu, which can also be accessed by pressing the menu key/button or on screen control as well.
Also included in this update is conversations view. It is said to help with reading emails since mobile devices usually have small screen space, though I haven't tested this view because I'm personally not a fan of conversation view in general.
The update is available now from Google Play.