As Cmdr Lovell [aka Tom Hanks] says in 'Apollo 13', when he's interviewed before the mission and he's asked what he foresees in the future: "I see a computer that will fit in a single room...".
There's also the bit when they have to calculate their emergency reentry angles etc using a pencil and paper and slide-rules... Then the guys at mission-control recheck the answers the same way calling check, check, check etc... Their 70's on-board computer was less than an 80's pocket-calculator and way below a modern cell-phone, let alone any modern computer..