4:10 ET: At the conclusion of Kagan's statement, Leahy adjourned the hearing until tomorrow at 9 am ET. Flashbulbs were again a-popping as she left the hearing room after greeting friends and supporters. (The noise makes the hearing room sound as if every person in it is crumpling a paper bag at the same time.)
Tomorrow, the senators will begin their questioning of Kagan. For the first round of questioning, each senator will have 30 minutes to ask questions of the nominee. Questioning will continue on Wednesday and possibly on Thursday.
That's all for the day, but come back to NBC's First Read tomorrow for our continuing live coverage of the confirmation hearings.
4:02 ET: More Kagan: "I will make no pledges this week other than this one - that if confirmed, I will remember and abide by all these lessons. I will listen hard, to every party before the Court and to each of my colleagues. I will work hard. And I will do my best to consider every case impartially, modestly, with commitment to principle, and in accordance with law."
4:01 ET: Speaking about her mentor Justice Thurgood Marshall, Kagan said: "Justice Marshall revered the Court - and for a simple reason. In his life, in his great struggle for racial justice, the Supreme Court stood as the part of government that was most open to every American - and that most often fulfilled our Constitution's promise of treating all persons with equal respect, equal care, and equal attention."
3:59 ET: Kagan thanked the women who have served on the court and offered her condolences to Justice Ruth Bader Ginsberg, whose husband passed away yesterday.
3:54 ET: Almost three and a half hours into the hearing, the nominee has uttered her first words of the day. The sound of camera shutters popping as she was sworn in was almost overwhelming.
3:50 ET: Brown, a Republican and a 29-year veteran of the Massachusetts National Guard, said in May that he was "satisfied" with Kagan's explanation of the issue of military recruitment at Harvard Law. (Read a report by NBC's Ken Strickland on that meeting here.)
In his remarks to introduce her today, Brown did not bring up that issue, nor did he allude to how he will vote on her confirmation. But he said that she is "undoubtedly a brilliant woman" and that he would be "proud" for the fourth woman to ever serve on the court to have such strong roots in his home state.
He added: "I look forward to Ms. Kagan’s responses to the committee’s questions. I know that I have some of my own, and I am quite sure that my colleagues here today do as well."
3:43 ET: Kerry said that the late Sen. Ted Kennedy would have been proud to introduce Elena Kagan. Kennedy was the longest serving member of the Senate Judiciary Committee for either party.
3:37 ET: Three hours into the hearing, Sen. John Kerry, D-Mass., has begun his remarks to introduce Kagan. After he and Brown speak, Kagan will offer her opening statement. (For a preview of what she'll say, click here.)
3:30 ET: Here's something you very rarely hear at a Senate hearing: The panel may actually be ahead of schedule. Kagan's opening statement was originally estimated to happen around 3:45p ET. Reporters are now being advised that her remarks could actually start a little bit earlier than that.
3:25 ET: Sen. Al Franken, D-Minn., is the last senator to speak. Like almost every member of the panel, he opened his remarks with a note about the legacy of Sen. Robert Byrd, who passed away this morning.
"I would have to serve until I was 118 years old" to serve as long as Sen. Byrd did, Franken noted. "I doubt that's going to happen."
3:19 ET: Sen. Scott Brown, R-Mass., has entered the hearing room. He will be joined by delegation colleague Sen. John Kerry to introduce Kagan before her opening statement.
3:15 ET: Sen. Amy Klobuchar, D-Minn. highlighted that Kagan - if confirmed - would be the fourth woman to ever serve on the high court. Klobuchar is one of just two women currently serving on the Senate Judiciary Committee.
3:14 ET: During the break, Republican Sens. Cornyn and Sessions fielded questions from reporters outside the hearing room. Both pushed back at Democrats' criticism of "conservative activism" on the part of the Roberts court, especially as illustrated by the Citizens United decision. (To read more about that case, click here).
Sessions called Democrats' description of the landmark decision "a distortion," and Cornyn warned that outcry about its consequences for the political process should be "taken with a grain of salt." Those who support the court's decision say that it upholds the First Amendment right to free speech.
The two Republicans were also asked about GOP members' description of the late Justice Thurgood Marshall as an "activist judge." Marshall, a civil rights icon who later became the first African-American to serve on the high court, famously argued the Brown v. Board of Education case as a lawyer for the NAACP. Asked if he believed that case -- which ruled unconstitutional the doctrine of "separate but equal" -- represented improprer "activism," Cornyn responded, "No, I do not."
2:57 ET: And we're back. Next up, Sen. Sheldon Whitehouse, D-R.I.
2:37 ET: A ten minute recess in the hearing means there's time for a history fact break!
Republicans are eager to discuss what President Obama's judicial nominations indicate about his governing philosophy. Per the Congressional Research Service: Of the 44 presidents in American history, 41 of them have had the opportunity to nominate someone to the high court. The three who didn't get the chance: William Henry Harrison, Zachary Taylor, and Jimmy Carter.
2:33 ET: The final members to speak before a well-earned 10 minute break in the hearing: Sens. Tom Coburn, R-Okla, and Sen. Ben Cardin, D-Md.
2:22 ET: Sen. Dick Durbin, D-Ill., echoed Schumer's criticism of "activism" on the part of the Roberts court. Referencing the name of a recent Supreme Court ruling that dramatically loosened limits on how corporations can advocate on the part of political campaigns, Durbin said to conservatives who warn of activism by liberal judges, "I have two words for you: Citizens United."
2:12 ET: The son of the late Justice Thurgood Marshall, for whom Kagan clerked, is in the hearing room today. Marshall was described as a "well-known liberal activist judge" by Republican Sen. Sessions earlier today. And Sen. Cornyn of Texas called Marshall an "unapologetic" activist judge.
2:08 ET: More Schumer: "She is straight out of central casting for this job."
2:05 ET: Sen. Chuck Schumer, D-N.Y., quipped that -- with thousands of pages of documents released by the Clinton Library in the weeks leading up to today's hearing -- the only thing that senators lack access to is Kagan's "kindergarten report card."
Schumer also took aim at the current court led by Chief Justice John Roberts, calling it a "highly fractured court with an often rarefied way of looking at the law." Citing recent decisions that some Democrats have criticized as too pro-business, he said that the court has been exercising "judicial activism to pull the country to the right."
1:57 ET: Graham said that he believes Kagan's blocking of military recruiters at campus placement centers at Harvard Law School was "inappropriate," but he adds that there will be more to discuss on the topic as the hearing progresses.
He also said that Kagan will have "a lot of explaining to do" about her naming of Barak as her "judicial hero."
Addressing those who have seemed "surprised" that Obama nominated a "liberal person," Graham said, "What did I expect from President Obama? Just about what I'm getting."
"At the end of the day, I think the qualification test will be met," he said. But he added that questions remain about whether or not Kagan can keep from "channeling" her political views while serving on the court.
1:52 ET: Sen. Lindsey Graham, R-S.C., is up next. He was the only GOP member of this committee to support Supreme Court nominee Sonia Sotomayor.
1:43 ET: Sen. Arlen Specter, D-Penn., is the ninth senator to speak. He was once the first member to deliver opening statements at hearings like this one; as a Republican, he chaired the committee between 2005-2007, but he lost his seniority on the panel when he changed parties last year.
1:37 ET: Several Republicans, including Kyl, have warned that Kagan's writings show that she would be a "results-oriented" judge who would make decisions based on her opinion of what the outcome of a case should be, regardless of the rightness of the judgment under the Constitution.
1:33 ET: Sen. Russ Feingold, D-Wisc., hinted at the fact that the court, while it has become more racially diverse over the last century, still lacks wide geographic diversity. (If confirmed, Kagan would be the fourth New Yorker on the court.)
Sen. Jon Kyl, R-Ariz., joked that he, too, hopes for more geographic diversity on the court, considering that it's been three years since a justice from his home state (retired justice Sandra Day O'Connor) served as a Supreme Court justice.
1:27 ET: Sen. Chuck Grassley, R-Iowa, says that Kagan's lack of experience as a judge is not "dispositive," but says that because she has not served on the bench, "it's even more critical that we are persuaded that you have the proper judicial philosophy and will practice it once confirmed."
1:18 ET: "Snoozefest?" Feinstein said that if this week's hearings aren't full of fireworks, it's a testament to just how qualified the nominee has shown herself to be.
1:15 ET: Sen. Dianne Feinstein, D-Calif. is next to speak. She praised Kagan's experience as Solicitor General and said "I believe that you are eminently confirmable."
Noting that Kagan has come under fire for never having served as a judge, Feinstein countered: "Frankly, I find this refreshing." All of the current judges on the Supreme Court served as federal appeals court judges before being nominated to the high court.
Feinstein also noted that she is "extremely dismayed" by today's Supreme Court decision regarding the Chicago gun ban, citing the decision as an example of a dramatic shift on the court in recent years.
1:08 ET: Hatch to Kagan: "Something tells me that this is going to be your last confirmation hearing."
1:05 ET: Sen. Orrin Hatch of Utah now giving his opening statement. He was one of two Republicans on the committee who voted to confirm Kagan as Solicitor General last year. (The other was Sen. Jon Kyl, R-Ariz.)
12:58 ET: In calling for Kagan to be transparent about her judicial philosophy, Kohl references a memo Kagan wrote in 1995, in which she called judicial confirmation hearings "a vapid and hollow charade."
Saying that Kagan's "judicial philosophy is almost invisible to us," he added that, while senators don't have the right to know in advance how she would decide particular cases, "we do have a right to understand your judicial philosophy and what you think about fundamental issues that will come before the court."
12:56 ET: Next up in opening statements, Sen. Herb Kohl, D-Wisc. Statements will proceed in order of seniority on the panel, alternating between Democratic and Republican members. There are 19 members of the Senate Judiciary Committee.
12:53 ET: More Sessions: Kagan has "associated herself with well-known activist judges" like Thurgood Marshall and Israeli Supreme Court Justice Aharon Barak. He says that President Obama "calls on judges to base their decisions on empathy and their broader vision of what America should be. He suggests that his nominee shares those views."
12:46 ET: Ranking member Jeff Sessions, who will lead the GOP argument against Kagan'sconfirmation, promises a fair and respectful hearing, goes on to cite Kagan's lack of judicial experience and her career path as a political aide in the Clinton White House among his "serious concerns" about her ability to serve impartially on the court.
12:40 ET: In his opening statement, Leahy urges Kagan to "be open, be responsive" and "to share with us and the American people her judicial philosophy and indicate her judicial independence."
"I believe that fair-minded people will find her judicial philosophy well within the legal mainstream," said the Vermont lawmaker.
12:33 ET: Opening the hearing, Leahy offered a tribute to the late Sen. Robert Byrd, who died this morning at the age of 92. He called Byrd "a mentor and a friend" and an example for future generations.
12:32 ET: The nominee was all smiles as she entered the hearing room. She's seated now and Chairman Leahy has gaveled the hearing to order.
12:15 ET: Live from Room 216 of the Hart Senate Office Building, we are live-blogging the confirmation hearing of Supreme Court nominee Elena Kagan. If confirmed, Kagan would be the 112th justice of the high court, and only the fourth woman to serve in the court's history.
The hearings are slated to begin at 12:30 ET, so check back to this space often to get the latest news. Here are five things that we'll be watching throughout the week as the debate unfolds.