GEOFF BENNETT: Former President Donald Trump's first criminal trial started today in New York City.

It's the first of four criminal indictments that Mr. Trump is facing.

It's an historic moment, the first criminal trial of any former president.

He faces 34 counts of falsifying business records to cover up an alleged extramarital affair that surfaced during his 2016 campaign.

Mr. Trump today cast himself as under attack, calling the trial a -- quote - - "political persecution."

Joining us now from New York is our William Brangham, who's been covering the former president's legal cases.

So, William, jury selection started this afternoon, but only after a good deal of sparring over various motions.

Walk us through exactly what happened.

WILLIAM BRANGHAM: Geoff, the day started out with a lot of conversation about the gag order that was placed on Donald Trump by this judge, Juan Merchan, and whether or not Trump violated it today or over this past weekend.

I mean, it's important to remember there's - - I cannot think of a criminal defendant in recent American legal history who has so aggressively and sometimes violently gone after the judges and prosecutors who are overseeing the cases that he is in the middle of.

And in this case, Donald Trump has gone after Judge Merchan, and particularly his adult daughter, quite a bit.

He has argued that because she worked for a Democratic organization that thus the judge should recuse himself from this case.

That is not happening, but the judge put a gag order on Trump back in March, expanded it last week.

But, still, today, Donald Trump was posting videos where one of his supporters was going after the judge's wife.

Over the weekend, Donald Trump at a rally was going after one of the key witnesses in this case, Michael Cohen, his former lawyer.

And the prosecutors argue that, Donald Trump, you are clearly violating this gag order, and they want the judge to issue some penalties, perhaps $1,000 per violation, whether that's a social media posting or something he says aloud in front of a camera.

The judge has said, in about 10 days, he will hold a hearing to go over those allegations.

GEOFF BENNETT: And there was additional debate today, William, over what testimony the jury should be able to hear.

What was decided on that front?

WILLIAM BRANGHAM: That's right, Geoff.

There -- the jury will not hear anything about the dozens of women who allege that Donald Trump sexually harassed or sexually assaulted them over the years.

Prosecutors wanted to introduce that, and the judge in this case said, no, that that was hearsay and gossip and he wasn't going to allow that.

The jury will hear a good deal of testimony about what is known as this catch-and-kill scheme.

And that is the mechanism where the publisher of "The National Enquirer" and Michael Cohen and allegedly Donald Trump had built this system so that, if people came forward backed during the 2016 campaign and made allegations about Donald Trump, that they would pay those people, basically catch their story and kill them, and so that they would not go forward and not get out into the public.

None of those are being charged in this case.

The Stormy Daniels hush money allegations are the only things at issue here.

But the prosecutors want to set up this -- that there was a recurring pattern of Trump and his associates to build a mechanism to squash cases like that.

So the jury will hear a good deal about former Playboy model Karen McDougal who, during the 2016 campaign, came forward to say: I have had a relationship with Donald Trump in the past.

And the jury will hear something about that.

GEOFF BENNETT: And, William, close to 100 people were asked to be jurors in this case, as I understand it.

Given the historic nature of it, all of the attention surrounding it, how do they go about finding the final 12?

WILLIAM BRANGHAM: Right.

Legal analysts argue that this is one of the most critical parts of any case, is deciding, who are those people that will sit in the jury box and hear this evidence?

The judge, as judges often do, has argued, he's going to go about it the old-fashioned way.

He's going to ask everyone if they can be impartial, if they can put their biases aside, listen to the evidence and make a judgment on this.

Today, though, there were 94, 96 people who were brought in as potential jurors.

And the judge has all along said, if anyone basically argues that they cannot listen to this evidence and be impartial, that I'm just going to let them go.

Shockingly, 50 people raised their hands today and said, I cannot listen to this evidence for whatever reason.

They did not give any reason for this.

And so they have all been excused.

And so the people who made it through that initial vetting process have been going through this 42-question questionnaire that asks basic things about where they live, their level of education, the kind of work that they do, but also asks things like, what kind of media do you listen to?

Have you ever been to a Trump rally?

Have you ever belonged to an organization that was anti-Trump?

Are you a member of QAnon or Antifa?

Things like that that try to get at whether or not they might have a clear political bias in all of this.

I mean, one of the very tricky parts that jurors -- that the prosecution and the defense have to be on guard for is anyone that might in that process not be totally honest and who they themselves may want to be on this jury, but because they have already made up their mind, and so that they want to either prosecute or exonerate Donald Trump.

So that's something that they're all going to be watching for.

Jury selection, they did not pick any jurors today.

Could be another couple of weeks before a jury is seated.

GEOFF BENNETT: That is William Brangham in New York City for us tonight.

William, thank you.