Now that more tablets can display desktop-quality websites, YouTube has changed its web version to match. The streaming site has updated its web interface to better support large touchscreen devices, such as iPads, Android tablets, and Chrome OS machines. New gestures allow you to swipe quickly in full screen mode or on the mini-player, while improved scrolling and larger icon sizes should be more intuitive. Even the usual three-dot menu (below the thumbnails) is now persistent instead of requiring a mouse over.
Regardless of what you use, you should also see a better sorted viewing history and sort the playlists by moving the videos to the top or bottom. Android Police understands that the changes were first visible in March, but are now more widely available.