Regarding Rosenstein, it's important because Rosenstein is the boss of Mueller since Session's recusal. If Rosenstein is fired, he'll be replaced by an underling (if he
resigned I believe Trump could replace him at will) who could fire Mueller. You may have often heard of Nixon's "Saturday night massacre" with reference to various Trump firings; if Trump fires Rosenstein, those comparisons - mere exaggerations at the moment - come roaring back to life.
The latest crisis was precipitated by
a NY Times article on Rosenstein, which revealed that last year, just after Comey had been fired (which prominently, had used a letter from Rosenstein justifying the dismissal) he had recommended to various FBI people interviewing to be FBI director to wear a wire when meeting with Trump, and pondered speaking with Sessions John Kelly (then the Director of Homeland Security) about invoking the 25th Amendment and removing Trump. Nothing came of it, it would seem. Flash-forward to Friday, when the times published this article.
This turned Rosenstein into a
dead man walking, and Rosenstein's removal seems to be
a matter of when, not if. Yesterday, rumors came out (
this Axios article appears to be the initial source) that seemed to imply that Rosenstein was either resigning or considering to resign, which quickly made the news circuits.
How true these are remain unclear: some suggest that he had decided to resign, or that he thought he would be fired, or some combination, or something else. More conspiratorial voices allege that the report was leaked in an attempt to force Rosenstein to resign and present a
fait accompli, and that when Rosenstein refused, it became this chaos. Regardless, Monday ended the same way it began: with Rosenstein still in office, and Mueller still working away.
Soon after, it came out that Trump would be meeting with Rosenstein on Thursday. What happens there, and after that, is unknown.