[Updated at 3:42 p.m. ET] After blessing the crowd, Pope Francis re-entered the basilica.
Here is video of his first public appearance as pope:
[Updated at 3:33 p.m. ET] The blessing is over, and the crowd roars.
Here's more about Pope Francis, the former Cardinal Bergoglio of Argentina: He is 76, and is considered a straight-shooter who calls things as he sees them, and a follower of the church's most conservative wing. He is a former archbishop of Buenos Aires.
He has clashed with the government of President Cristina Fernandez de Kirchner over his opposition to gay marriage and free distribution of contraceptives.
Besides being the first non-European popein the modern era, the first South American pope and the third straight non-Italian pope, he also is the first Pope Francis.
[Updated at 3:30 p.m. ET] Pope Francis has offered his blessing "to you and to the whole world." This is known as the "Urbi et Orbi" (to the city and the world) blessing.
[Updated at 3:29 p.m. ET] Pope Francis says he will shortly offer his blessing, but now he's asking the crowd to have a moment of silence to pray for him.
[Updated at 3:27 p.m. ET] Pope Francis says from the balcony (according to an English translation):
"As you know, the duty of the conclave was to appoint a bishop of Rome. It seems to me that my brother cardinals have chosen one who is from far away, but here I am.
"I would like to thank you for your embrace, also to ... the bishops, thank you very much.
"First and foremost, I would like to pray for our emeritus pope, Benedict XVI. Let us pray all of us together … so that he's blessed by the lord and guarded."
Pope Francis then said the Lord's Prayer.
[Updated at 3:23 p.m. ET] Bergoglio, the new pope, has chosen the name Francis, according to Vatican Radio. He's now appearing on the balcony.
[Updated at 3:20 p.m. ET] Bergoglio is the first pope from outside of Europe in the modern era, the first South American pope, and the third straight non-Italian pope.
(Correction notice: This post initially said that Bergoglio is the first non-European pope. We've corrected that to say he's the first non-European pope in the modern era.)
[Updated at 3:15 p.m. ET] And the new pope is: Argentina's Cardinal Jorge Mario Bergoglio.
[Updated at 3:12 p.m. ET] The protodeacon is on the balcony, making the announcement.
[Updated at 3:08 p.m. ET] It is taking longer for the new pope to appear after the white smoke this year than it did for Benedict XVI to appear after his election in 2005. But, an extra step has been added this time - the new pope has been allowed to pray alone in the Pauline Chapel before he appears on the balcony.
That could account for at least some of the difference.
[Updated at 3:03 p.m. ET] It will be interesting to learn not only who the new pope is, but also what name he has chosen for himself. Popes often take a regnal name (like Benedict) that a previous pope used, and it generally is meant to point to a tone that the new pontiff wants to set, CNN senior Vatican analyst John Allen says.
For example, Pius XII, who served from 1939 to 1958, was very conservative, eminent Italian church historian Alberto Melloni told CNN. So, "if the new pope was to call himself Pius XIII, it would be a very ideological choice," he said.
Read more about what a pope's chosen name indicates, from CNN's Laura Smith-Spark.
[Updated at 2:48 p.m. ET] Here's what we're going to hear from the cardinal who will introduce the new pope:
"Annuntio vobis gaudium magnum: Habemus Papam! Eminentissimum ac Reverendissimum Dominum, Dominum (FIRST NAME OF NEW POPE) Sanctae Romanae Ecclesiae Cardinalem (LAST NAME OF NEW POPE) qui sibi nomen imposuit (POPE’S NEW NAME)."
"I announce to you a great joy: We have a pope! The eminent and most reverend lord, Lord (FIRST NAME OF NEW POPE), Cardinal of the Holy Roman Church (LAST NAME OF NEW POPE), who has taken the name (POPE'S NEW NAME)."
[Updated at 2:41 p.m. ET] CNN senior Vatican analyst John Allen, on the moment that we will see the pope on the balcony of St. Peter's Basilica: "First impressions last. ... It will be very interesting to see how the new pope comports himself here tonight and makes his introduction."
[Updated at 2:38 p.m. ET] It shouldn't be long before we find out who the new pope is. When Benedict XVI was elected in 2005, about 45 minutes passed between the appearance of the white smoke and the appearance of the cardinal who introduced the new pope.
Today, the smoke appeared just after 2 p.m. ET (7 p.m. in the Vatican).
[Updated at 2:30 p.m. ET] The crowd at St. Peter's Square continues to swell. "People are literally running up the block (so they can see the pope) when he comes out on the balcony for the first time," CNN's Anderson Cooper reports from the Vatican.
[Updated at 2:25 p.m. ET] From CNN's Jim Bittermann at the Vatican: The crowd waiting for the new pope represents all sorts of nationalities – "everybody from around the world."
"You see a lot of religious folks are here, different orders of nuns and priests, packing in all afternoon," as well as tourists, he said. "There are more people just as I'm speaking. All of the sudden there's been a surge of people coming in."
[Updated at 2:23 p.m. ET] Like the one in which Benedict XVI was chosen in 2005, this election didn't take long. The white smoke comes on just the conclave's second day.
We have a few steps to take before we learn who the new pope is. Here's what we've been told will happen next:
– The new pope will leave the Sistine Chapel to put on his papal robes, then re-enter the chapel for prayer with the cardinals.
– The cardinals will then line up to congratulate the new pope and promise their obedience to him.
– The pope will then go back to Pauline Chapel to pray for a few moments.
– Only then will the pope prepare to reveal himself to the public. At the balcony of St. Peter's Basilica, proto-deacon Cardinal Jean-Louis Tauran (assuming Tauran himself wasn't elected) will appear and announce the new pope's old name, and the name he will be known as from now on.
– The pope will then appear on the balcony.
[Posted at 2:09 p.m. ET] White smoke above the Sistine Chapel have made it official: The Roman Catholic Church has a new pope.
Bells are ringing at the Vatican, and thousands of people gathered in the square are cheering.
We'll find out in the minutes to come who the new pope is. Stay with us as we find out.