Wire transfers (which meant Morse-code type transfers over the wire) and these go quite a ways back.
Before that? Good
Then one bank would transport its ledger and credits/debt notes across the country, ocean, etc. to do correspondent settlement with the other bank (which is how the entire merchant banking system was setup).
Read up how Giovanni di Bicci de’ Medici did this (Giovanni di Bicci de’ Medici – Wikipedia)