I'm going to throw this in here, because I think it's relevant based on Kelly's example of those horrible fires in Hawaii last year.
When I worked for one of AT&T's predecessors in the late 1990s/early 2000s, I had the opportunity to talk with one of the techies at what was then called Cingular Wireless. With the 1994 Northridge earthquake still relatively fresh in my mind, and how relatively useless the POTS network had been for the first day or so afterwards, I asked him what effect such a disaster would have on the cellular service network.
He told me that SMS (which is the acronym for, logically enough, Short Message Service) uses the voice network to send and receive, so it would be somewhat impacted by heavier call volume. And with a lot of people trying to make voice calls all at once, that would slow down that network and result in a lot -- probably the majority, he said, based on what he thought would be the demand under the circumstances -- of calls not being completed.
BUT because SMS sends in "bursts", it can take advantage of extremely short gaps in bandwidth availability ... fractions of a second, in fact, and send/receive during those gaps. So you would have a much better chance of getting a text out than trying to call for help. (He did still impress on me the need for the public to confine itself to urgent emergency messages to make the use of those gaps more efficient.)
Bear in mind, this was still the era of flip phones, but the SMS technology still works the same way with smartphones.
Extrapolating what he said to the present, if during an emergency the Internet was still up and there was still power to your modem and router, you could probably -- if your carrier allows -- switch to Wi-Fi calling and it would improve your ability to send/receive texts. Going further, I think this makes a good case for subscribing to any governmental emergency alert services (for example, I have UC Berkeley's MyShake app on my phone, which can send earthquake alerts for temblors of magnitude 4.5 or greater).
Unfortunately, data service is the first thing that will drop on cellular service in these situations, which renders things like Google Maps worthless, so unless you live in an area where the authorities can send text alerts of road closures and the like, you would be SOL there. Of course, I have always been a believer in following official instructions about evacuations anyway ...