T.37

T.37 is an ITU standard which deals with sending fax messages using email. It is also referred to as "Internet fax" or "Store-forward-fax".
A fax machine supporting T.37 will send a fax to an email address by converting the document to a TIFF-F image, attaching it to an email, and sending the document. The destination fax receives the email and prints the attached document.
To interface with regular fax machines:

T.37 can be used in conjunction with fax gateways to communicate with regular fax machines. The fax gateway converts emails to regular faxes or regular faxes to emails.
A T.37-compliant fax machine includes legacy fax functionality to send to regular fax numbers and requires a phone line for this.
To find the destination faxes email address, the RFC 4143 standard is in development, which allows a fax machine to use a destination fax number to look up an alternative email address.