The F.B.I. wouldn’t be investigating Mr. Trump’s aides without evidence of wrongdoing, right?

Yes and no. The F.B.I. has the authority to investigate crimes, but the mere fact that agents are looking at Mr. Trump’s aides does not mean they can prove wrongdoing. In fact, American officials have said there is no proof of collusion between Russia and the Trump campaign. Still, current and former officials say they have uncovered evidence that Mr. Trump’s associates were in repeated contact with Russians. The F.B.I. is scrutinizing those contacts.

What kind of measures will the F.B.I. take during its investigation?

It is hard to say because nearly everything that counterintelligence agents do is classified. Even their investigative methods are considered too secret to make public. The New York Times has reported that some of the evidence uncovered so far came from intercepted conversations between officials inside the Kremlin who discussed their meetings with Mr. Trump’s associates. The United States, like other countries, also has a worldwide network of paid informants who provide information about the inner workings of foreign governments. And the F.B.I. has access to waves of reports from other intelligence agencies and foreign allies.

Mr. Trump said he was wiretapped. How does that fit into this?

It doesn’t, really. In a barrage of tweets this month, Mr. Trump accused President Barack Obama of having him wiretapped at Trump Tower during the campaign. That claim has since been rejected by Mr. Obama and all corners of the federal government. Mr. Comey and the director of the National Security Agency, Adm. Michael S. Rogers, said definitively on Monday that there was no evidence that such eavesdropping occurred.

Whether calculated or not, Mr. Trump’s Twitter posts provided a confusing distraction in the discussion about Russian interference. Though the claims have been widely rejected by Mr. Trump’s own national security officials, the White House stands by them and believes that the president will be proved correct. But some members of the House and Senate Intelligence Committees from both parties have indicated that no evidence exists — and that they will focus instead on questions of Russian meddling in the election.

What could come of Republican lawmakers’ calls for the F.B.I. to crack down on national security leaks? Mr. Comey declined to say whether the bureau was conducting any leak investigations. But he talked repeatedly about the seriousness raised by these types of disclosures, giving the impression that the F.B.I. will be investigating them.