Can you tell me about Carter, Reagan, and Iran?

I was a in Jr. High when Carter was the US President. I’ve stated before that my knowledge of history is terrible, although, I actually lived through this part of history. Still, I have a week understanding of international politics during that time.

On the recent Republican Presidential debate one of the candidates brought up the hostages in Iran being set free the day Reagan became President. I had always thought that was very suspicious. The candidate stated it with pride, implying the Republicans are better than the Democrats I guess. What exactly happen with the hostage situation? It seemed to me like possibly the Republicans at the time were happy to let the hostages sit captive until the Presidential oath was taken so Reagan would look good. Is that wrong?

I know almost everyone thought Carter was a bad President, but didn’t he help broker peace between Egypt and Israel, which as far as I know held pretty well.

Note: when I say the Republicans, I mean “the party” not all Republicans as individuals.