Google Hangouts has been a depressingly central part of my life for years now, but the web interface has always felt a little hacked-together. Today, all that changes, with a redesigned interface, and a dedicated homepage for Hangouts.
The new URL follows Google's normal naming convention: hangouts.google.com. The new homepage works like an expanded version of the existing Hangouts interface: there's a list of contacts on the left, and your conversations expand out as separate tabs on the right.
Don't worry, though — if you're wedded at the hip to having Hangouts in Gmail, that's still an option, as is the Hangouts desktop app. But if you're a fellow thousand-tab warrior, the new Hangouts should fit right into your workflow.