Confused regarding routers/modems

I recently completed a networking course, and up until now I have been confident in my knowledge.

Throughout this course, however, modems were not once mentioned, and I had no idea they existed. I was led to believe that routers handled all communication with the internet, so that the structure of a simple network would be:

Internet –> Router –> Switch –> Hosts

Doing my own research, it seems as though modems are in fact the devices that communicate with the internet, whereas routers simply route within a LAN, which leaves me extremely confused as I was under the impression that was the job of the switch.

So my question is, what purposes do routers and modems serve in a network?

Thank you.