My tablet has a built-in cellular Internet connection. This has come in quite handy, especially since I can turn it into a mobile hotspot with a click.

Keep in mind that cellular networks may be available but saturated in an emergency. In that case, regular text messages are the most likely to get through, followed by short Internet messages. Voice calls, I suspect, may be very hard to make.

If wired and cellular Internet is down, you're out of luck unless you have a satellite Internet system, you subscribe to a local Wireless ISP (typically using point-to-multipoint non-cellular radio services, also typically with very limited service areas) or some other radio-based system.