Picture-in-picture means you can bring up a settings menu and scroll through in a separate window while your video keeps playing. So you won't have to stop watching 'The Grand Tour' to tweak the app's settings, for example.
Time-shifting, meanwhile, lets you pause and rewind live video, much like you can with a dedicated set-top box.
Apps can also record content, including scheduling that can grab content automatically. While it doesn't mean you can record video straight from your streaming apps, it does empower the new Fire TV with DVR-like skills.
This is all because the Fire TV runs on Fire OS 6, which is built on Google's Android 7 Nougat mobile operating system.
However, don't expect Amazon's older streaming devices to get the same skills. The firm says there are no current plans to upgrade older hardware to the same software. So if you want the new features, you'll have to spend £70 on a new Fire TV.