A modem and router work in tandem to deliver you an internet connection and then grant access to your various devices.

You can do tons of stuff with a computer that most hardware NAT-routers cannot do, like having firewall software run on it, provide services (print (I know the SMC routers also have this), file, proxy ...

Security researchers analyzed nine popular WiFi routers and found a total of 226 potential vulnerabilities in them, even when running the latest firmware. The tested routers are made by Asus, AVM, ...