Just like the favorites menu, opening the history will now prompt a pop-up window to appear, rather than taking you to a full page showing your history. Because of that, the history option is no longer a dropdown, since you can open a more complete experience easily by clicking it. Just like favorites, you can pin the history to the side of the screen so it's always accessible, and you can also now add the history icon next to the address bar.
The history window features a few pivots - All, which shows all your history; Recently closed, which has the tabs you closed most recently; and Tabs from other devices, assuming you have history and tab sync enabled, though this is still only available to some users. The browser also remembers the pivot you used last, so you'll be taken to it next time you open the history.
One of the improvements you get with this pop-up window is that the websites you open will be visible behind it without closing the window, so you can more easily open various links and make sure they're the right ones. Microsoft has also improved the logic for recently closed tabs, so Edge will remember the last 25 tabs and windows you've closed in past sessions, rather than only remembering the last session.
As usual, this experience is available first to members of the Edge Insider program, specifically those in the Dev and Canary channels. It should come to everyone over time.