UUCP [https://en.wikipedia.org/wiki/UUCP] used the computers' modems to dial out to other computers, establishing temporary, point-to-point links between them. Each system in a UUCP network has a list of neighbor systems, with phone numbers, login names and passwords, etc.
FidoNet [https://en.wikipedia.org/wiki/FidoNet] was a very popular alternative to internet in Russia as late as 1990s. It used temporary modem connections to exchange private (email) and public (forum) messages between the BBSes in the network.
In Russia, there was a somewhat eccentric, very outspoken enthusiast of upgrading FidoNet to use web protocols and capabilities. Apparently, he's still active in developing "Fido 2.0": https://github.com/Mithgol