Updated on June 10 at 7:32 p.m. ET

So now that former FBI Director James Comey has appeared before a Senate committee and accused the White House of lying about his firing — and, in the process, raised significant questions about obstruction of justice — what happens next?

A lot.

In a surprise announcement Saturday evening, Attorney General Jeff Sessions bowed out of planned hearings about the Justice Department's fiscal year 2018 budget proposal set for June 13 on Capitol Hill, sending Deputy Attorney General Rod Rosenstein in his place.

Instead, Sessions said in letters to lawmakers, he will appear before the Senate Intelligence Committee. "In light of reports regarding Mr. Comey's recent testimony ... it is important that I have an opportunity to address these matters in the appropriate forum," Sessions wrote, pointing to the committee's ongoing Russia investigation and access to information.

While Sessions' testimony Tuesday has the makings of another high-profile event, much of the next phase of the various investigations will likely not be as clear-cut and straightforward as the drama of congressional hearings carried live with millions watching on television and online.

The Senate and House Intelligence Committees will continue to sift through raw intelligence materials, and interview witnesses, behind closed doors in secure rooms. And special counsel Robert Mueller's team will conduct a criminal investigation that, based on Mueller's reputation, likely won't produce many leaked tidbits or updates to the outside world.

Here's what we do know will happen next with the multiple investigations digging into what Russia did to influence the 2016 presidential election, and into whether any Trump campaign associates collaborated with those efforts.

The Senate Intelligence Committee

After Comey's hearing Thursday, Committee Chair Richard Burr, R-N.C., said that at some point in the coming days, he and Vice Chair Mark Warner, D-Va., will meet with Mueller's team to discuss how the Senate can continue its investigation without interfering with Mueller's separate criminal probe.

The general concern is that the Senate committee could potentially make the special counsel investigation more difficult, by requesting evidence or interviews from people who may be key witnesses for Mueller.

Grants of immunity — a key part of both criminal and congressional investigations — are a key area where coordination would be needed.

In the immediate aftermath of Mueller's appointment, several key Senate Republicans, like Lindsey Graham of South Carolina and John Cornyn of Texas, suggested the House and Senate Intelligence Committees may need to slow down their efforts, in order to stay out of the special counsel's way.

Burr asked Comey about that Thursday. "Is there any doubt in your mind that this committee can carry out its oversight role," he asked, "in parallel with the — now — special counsel that's been set up?"

"No — no doubt," Comey responded. "It can be done. It requires lots of conversations, but Bob Mueller is one of this country's great, great pros. And I'm sure you all will be able to work it out with him to run it in parallel."

The Senate committee recently received documents from former national security adviser Michael Flynn, in response to a subpoena. All along, Burr and Warner have said they plan to meet with Jared Kushner, a top White House adviser and President Trump's son-in-law.

Several media reports indicate that conversation could happen in the coming weeks.

Separately, the Senate Judiciary Committee has asked Columbia Law School professor Daniel Richman to turn over his copies of Comey's memos about his meetings with President Trump. During his Thursday testimony, Comey told lawmakers he provided the documents to Richman, and instructed his friend to share the memos' details with the New York Times.

In the Senate Intelligence Committee hearing, Arkansas Republican Sen. Tom Cotton asked Comey if he would encourage Richman and the Department of Justice to share the memos: "Sure."

And Friday evening, Sen. Dianne Feinstein, D-Calif., the ranking member of the Senate Judiciary Committee, recommended that the committee investigate "all matters relating to obstruction of justice and use its subpoena authority if necessary," after testimony in the Senate Intelligence Committee earlier in the week from Comey and four other current intelligence chiefs.

The House Intelligence Committee

The House investigation is facing the same "deconfliction" challenges its Senate counterpart is, when it comes to making sure to stay out of Mueller's way.

The committee has issued subpoenas for "testimony, personal documents, and business records" to both Flynn and Michael Cohen, one of Trump's personal attorneys. Additionally, the committee has subpoenaed former Obama administration officials John Brennan, Susan Rice, and Samantha Power, in relation to the question of whether intelligence information was improperly shared or distributed for political purposes.

And on Friday, the committee sent a letter to Comey requesting any notes or memoranda "memorializing discussions Comey had with President Trump."

The committee sent a second letter to White House Counsel Don McGahn, requesting, as a press release put it, "he inform the committee whether any White House recordings or memoranda of Comey's conversations with President Trump now exist or have in the past." Of course, this is a reference to Trump's tweet warning Comey that there may be "tapes" of their conversations. If there are tapes, the committee asked McGahn to turn them over by June 23.

Former Homeland Security Secretary Jeh Johnson will also likely testify before the committee, though a date has not been set yet. Adam Schiff, the top Democrat on the committee, said the goal would be to hear from Johnson about what sort of warnings about potential Russian cyberattacks the Department issued to state election officials in the run-up to Election Day.

The Department of Justice special counsel

We don't know too much about where Robert Mueller's special counsel investigation stands. And based on Mueller's reputation for keeping developments out of the headlines, we don't expect to anytime soon.

Comey did tell the Senate Intelligence Committee that he handed his memos about meetings with Trump over to Mueller's office. He also indicated multiple times that he believed that as part of his probe, Mueller is investigating whether or not any obstruction of justice took place after the initial federal investigation into Russia meddling began.

One thing we do know about the Mueller investigation is the lawyers he has brought onto the team. When Mueller initially took over the FBI's investigation, he enlisted the help of prosecutors with deep experience investigating corporate fraud, Watergate and the mafia, among other matters.

According to the National Law Journal, Mueller has now added another high-profile lawyer to his team: Deputy Solicitor General Michael Dreeben, who's one of the most respected lawyers within the Department of Justice.

The Trump wild card

On Thursday, Comey told lawmakers that he decided to tip the media off about Trump's "let this go" comment only after Trump tweeted about the possibility of a recording device inside the Oval Office.

Comey's move was just the latest significant develop in the Russia investigation to spring directly from unilateral, unprompted actions by President Trump.

Trump has repeatedly raised the profile — and the stakes — of the congressional and criminal investigations through his actions. The most significant example of this was his decision to fire Comey.

Other key moments include the "tapes" tweet, and a tweet accusing President Obama of ordering an illegal wiretap of Trump Tower during the presidential campaign. That's an accusation that the House Intelligence Committee, Senate Intelligence Committee, Comey, and other officials all say was made without any factual basis.

Trump's personal lawyer in relation to the Russia probes, Marc Kasowitz, has indicated he'll file complaints with both the Department of Justice and the Senate Judiciary Committee related to Comey's decision to feed information about his Trump memos to the New York Times via an intermediary.

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