You attach for example a PDF file with the invoice, including bank account number etc. The person receiving the invoice logs into his or her online bank and pays it.

Since decent online banks will let you save the details of recipients, in practice it is very smooth and uncomplicated.

You could also receive and send invoices by fax, and there's nothing wrong with that.

In many cases that is just the bank printing a check that is mailed to the recipient.

Sure, it works. But it's super slow and archaic. In the same way some people think people writing personal checks works, but others think its ridiculous.

That's not how the invoices I receive or send are. They are real invoices with specification, sum to be paid, who to pay it to and date to pay. So let's take a bog-standard example: Your phone bill. Get the invoice in your e-mail, see what amount they want, log in to the bank, select them as the recipient, fill in the sum and paste the reference number. Assuming you're saving recipients in your online bank.

There's nothing slow or archaic about that, at least I haven't noticed that after a few thousand invoices sent and received by e-mail. With modern banks you can even make batch payment of invoices by uploading a csv file.