What was the Y2K bug and did it actually cause any real damage or was it all just panic?

Everyone remembers the warnings that the world was supposed to collapse at midnight on January 1, 2000 because computers could not handle the year change. Then nothing happened and people laughed it off as mass hysteria. But was Y2K actually a real threat that was fixed through a massive global effort, or was it genuinely overhyped from the start? How much did it cost to fix and who paid for it? And is it true there is a similar problem already coming in 2038?