Some systems are not monitored, and rely instead on a siren that alerts neigborts to a problem - until you have so many false alarms in your neighborhood, that the siren is just ignored. Most effective alarm systems utilize remote monitoring, by subscription from an alarm monitoring service, or from a patrol service. How signals get to this service is an important distinguishing factor between systems.
Othern than very recent systems, most monitoring is accomplished through phone lines. You alarm calls the monitoring service when a fault is detected, and a modem is used to communicate information about the alarm. If you phone line is inoperative, then the signal does not get through, and no one responds. It used to be that your phone line would likely only be inoperative if the line were cut, but in recent years there are many more reasons for you phone line to be inoperative. If you use voice over IP, and your power is out, or if you internet service is down (how often does that happen, as compared with plain old telephone service (POTS).
There are wireless monitoring options available for some alarm systems, but subscribing to this option will usually cost quite a bit extra.