How much storage does the Apple TV have?

The Apple TV no longer has any internal storage. Some of the early models did, but that has been discontinued. The Apple TV can stream media from your iOS devices like your iPhone, iPad or iPod Touch, as well as from your Mac or PC. Anything you want stored, you would store on one of these devices. You can also access your iCloud account from Apple TV, so that is another storage alternative. Any media you stream from subscription services such as HBO Now, Netflix, Hulu, etc., is stored on their servers, not on your local hardware.