With a side featuring two survivors of the 1958 Munich Air Disaster, Matt Busby's men defeated Benfica 4-1 at Wembley 10 years later.
From that team, Alex Stepney, Paddy Crerand and John Aston Jr, have all appeared on the UTD Podcast and their tales provide superb listening, as they tell us about a team that defied all the odds to reach the pinnacle of European football.
You can find quotes from the trio of legends below, as well as links to their episodes - simply click their names to listen.
JOHN ASTON JNR
Named Man of the Match for his outstanding contribution throughout the 1968 final, winger John Aston Jnr followed in his father's footsteps as he represented his boyhood club and shared the star-studded dressing room with talents including Nobby Stiles, George Best and Bobby Charlton.