Fax is scanning an image at one end of the communication, and sending the result to the other end, where it will be transformed back into an image.
However impossible it might seem, faxing was invented and patented before voice telephony. The first commercial faxing service was introduced in 1865 between Paris and Lyon. The first desktop fax machine for end users was introduced in 1948, while the 80s saw mass market distribution of compact fax machines very similar and completely compatible with today's models.
Every office still has a fax machine, or a fax server. Modern faxing is governed by the International Telecommunication Union (ITU) standard T30, which is ubiquitous, very reliable (that is, 99% or better completion rates between fax machines connected to PSTN), and is required by law for many legal document transmissions in many countries.