Andrew Banchich spotted a new Gmail feature that lets you record calls. I don't see the call record button in my account, so it's probably an experimental feature that's not yet widely available.
It's similar to the call recording feature from Google Voice. "In order to record your call, simply press 4. You can do it when you first accept a call, or any time after it's started. To stop the recording, press 4 again or hang up. Your recordings are saved online and you can access them just like you do with voicemail." Instead of pressing 4, you click the record button.
Death E-mails Google - New Yorker (blog)
3 hours ago