Any detector worth its salt should have a backup battery and work during a power outage. (Always check before buying one, of course, just to be sure.) If you have a monitored smoke detector or carbon monoxide detector, it should still work locally when the phone line’s down (meaning that you should hear it in your home). But depending on how it’s set up, it may not be able to communicate with the fire department or other emergency responders. You might have to make those calls yourself. Check out our reviews for smoke detectors and carbon monoxide detectors to learn more.