If you're watching a YouTube video on your Android phone and pause it then move to another app, you may start seeing a new notification. It will offer you the option to resume playback, not on your phone but on your TV. Obviously you need to have a Chromecast-connected TV or an Android TV on the same network for this to work.
The notification popped up for me yesterday while I was in bed catching up on the Champions League goals, but I dismissed it since I was away from the NVIDIA SHIELD in my living room. Fortunately our tipster got it, took some screenshots, and tried it. The notification can be expanded and turned off, if you don't want to see it again, or if you tap it, it'll turn on your TV and continue playing there. The notification will then obviously switch to the now playing interface with media controls.
This is super neat, as it makes it very easy to go from watching something on your phone to casting it on a big screen. I know you can manually cast within the YouTube app, but this is more a convenient anticipation of what you may want to do next. It's also the first time I see Google offering to resume playback on a different medium. I want this for music too.
Both our tipster and I saw the notification yesterday for the first time and are on the slightly older YouTube version 12.44.53 (APK Mirror), so it might be a server-side switch but it could have rolled with that version 3 days ago and we just happened to spot it. I'm not home now so I can't test to see if it works with the newer 12.44.56, but odds are it should as well.