My rabbi and I were recently studying in tractrate B'rachot and came across a story with more drama than you usually find in the talmud. (This story was, of course, not new to my rabbi. This is on B'rachot 27b-28a.) It's described in the commentary as one of the more famous stories in the talmud, but it was mostly new to me. (A tiny part of it shows up in the Pesach haggadah.)
First, some context that I'm distilling from a footnote in the Schottenstein edition, which they in turn distilled from Dorot HaRishonim by R. Yitzchak Isaac HaLevi, whoever that is. (Yeah, that's what it says in the note -- Yitzchak Isaac.)
These events occurred after the destruction of the temple by the Romans. As a last-ditch effort to preserve Judaism in its then-present form, the rabbis evacuated the Sanhedrin to Yavneh, with permission of the Romans. This new court (called the Mesivta), like the Sanhedrin before it, was headed by two scholars, the Nasi and the Av Beit Din. The former ranked the latter. Rabban Gamliel was the Nasi, installed into that position when the Mesivta was established after the previous Nasi didn't get out alive from Jerusalem. The first Av Beit Din was Rabbi Yochanan ben Zakkai, who was the one to petition the Romans; he died about eight years later and was succeeded by Rabbi Yehoshua.
So in the aftermath of a national calamity we have new leaders trying to re-establish authority and carry on. With that as context, on to the story:
A student once went to Rabbi Yehoshua and asked: is the evening prayer required or optional? R. Yehoshua said it is optional. The student then went to Rabban Gamliel and asked the same question; Rabban Gamliel said it is required. The student said that R. Yehoshua had said otherwise. Rabban Gamliel told the student to wait until everyone came to the study hall and repeat his question then.
As directed, the student rose to ask his question in front of the assembled rabbis and Rabban Gamliel answered. He then asked: is there anybody here who disputes this answer? R. Yehoshua said no. Rabban Gamliel, apparently unwilling to leave matters alone, or insisting on intellectual honesty, said: that's not what I heard; stand and let them testify. R. Yehoshua stood and said: I can't deny it; he's right here. Ok, I said that. (If you haven't figured it out by now, I am paraphrasing.)
Rabban Gamliel continued lecturing without allowing R. Yehoshua to sit (an act of humiliation). The people present began to murmur objections and finally told him to stop. They then related other incidents where Rabban Gamliel had tormented R. Yehoshua, including the famous one about the date of Yom Kippur (ask if you want me to elaborate), and finally the group concluded that it was time to depose Rabban Gamliel for bad behavior. (It is not clear to me how much of this discussion was right there in the study hall in front of Rabban Gamliel.)
This raised the question of whom to replace him with. R. Yehoshua would under other circumstances be a logical choice, but he's involved in the controversy so it can't be him. They settled on R. Elazar ben Azaryah because he was wise, wealthy, and of good lineage (which would protect him from retribution from Rabban Gamliel, the text says).
When they asked R. Elazar he said he had to consult his household. He asked his wife, who pointed out that he has no white hairs (that is, he's young and doesn't look the part), at which point a miracle occurred and the 18-year-old Elazar sprouted white hairs in his beard. Taking the presumed divine hint, he accepted the position.
The day he took charge R. Elazar removed the door-keepers from the study hall; all who wanted to could now come and listen. (This might bring to mind the famous story of Hillel's quest to learn torah even though he had no money to pay admission. Hillel was, by the way, an ancestor of Rabban Gamliel.) He also had more benches added to accommodate the influx. Also on that day, there was (miraculously?) not a single matter that they were not able to resolve; they even ran through the backlog of matters that had been deferred for Eliyahu to sort out when the moshiach comes. They were on a roll. (Apparently they did not record those answers for us, however...)
Also on that day Rabban Gamliel answered a student's question only to be contradicted by R. Yehoshua. They argued it out and R. Yehoshua won based on the merits of the argument (apparently not just due to the new power dynamic). Rabban Gamliel later decided that this meant God was with R. Yehoshua and he'd better go apologize, which he went and did, and after they exchanged heated words R. Yehoshua forgave him. R. Yehoshua first sent a messenger to the Mesivta but they wouldn't let him in, thinking that Rabban Gamliel was harassing them; then R. Yehoshua went himself, reported that they had reconciled, and said that Rabban Gamliel should be reinstated. (Rabban Gamliel was not then present.)
This put the rabbis in a bind. They couldn't remove R. Elazar after elevating him to the position of Nasi, because in matters of sanctity we only elevate, not downgrade. (R. Elazar, unlike Rabban Gamliel, hadn't done anything wrong. Not only that, but things were going well under him.) They then talked about time-sharing options, eventually deciding that R. Elazar would lecture one week in four and Rabban Gamliel the other three. (Not covered here is how policy decisions like opening the study hall would be made.)
At the very end of the story the g'mara tells us the identity of that student who asked the original question of both rabbis: it was Rabbi Shimon bar Yochai, to whom the kabbalistic work the Zohar is attributed.