Why two digits
In the 1960s and 1970s memory was very expensive. Saving two characters in every date meant big savings. Programmers did not believe their programs would still be running 30 years later.
Needless panic?
Because almost nothing happened, some people claim it was an overblown panic. Experts reply that nothing happened precisely because of the fixes. Minor bugs did appear, for example websites showing the date “1 January 19100”.
Next in line
Unix systems count time in seconds since 1970. In a 32-bit number this overflows on 19 January 2038. Most systems have been fixed, but old devices may still bring surprises.