Gemara

7b (Beraisa): We bless Birkas Chasanim all seven days with 10 people.

(Rav Yehudah): This is when there are Panim Chodoshos (new people) at the meal.

8a: Rav Ashi came to Rav Kahana's house. The first day he made all the Berachos.

After the first day, if there were Panim Chodoshos he would bless all the Berachos. If not, he blessed only "...sheha'Simchah bi'M'ono (that joy is in His dwelling)", and "Asher Bora Sason (Who created joy...)"

Rishonim

The Rif and Rosh (1:13) bring our Gemara.

Ran (DH v'Hu): Panim Chodoshos are people who were not there the day before. The Ramban says that it suffices for the Panim Chodoshos to be there, even if they did not eat. Tosfos says that if the Panim Chodoshos came at night we bless at night and during the day, as long as they were there at the time of Berachah. R. Tam says that Panim Chodoshos are people over whom the Bnei Chupah rejoice.

Rambam (10): If there were Panim Chodoshos who did not hear the Berachos of Nisu'in at the Nisu'in, we bless for them after Birkas ha'Mazon the seven Berachos like we bless at the Nisu'in. This is if there are 10, including the Chasanim.

Kesef Mishneh: It seems that the Rambam holds that even at the first meal on the first day we bless Sheva Berachos only if some people who ate did not hear the Berachos at Nisu'in. The Ramach says that there was an enactment of Birkas Chasanim at meals. It is improper for Birkas Nisu'in to exempt Birkas Chasanim, even if everyone at the meal heard Birkas Chasanim at the Nisu'in.

Rosh (1:13): 'Panim Chodoshos' are those who were not at the Chupah. It seems that this is only people for whom we increase the Simchah. A Medrash teaches that Shabbos is considered Panim Chodoshos. "Mizmor Shir l'Yom ha'Shabbos" - Hash-m said, Panim Chodoshos have come. It is normal to have extra Simchah and courses on Shabbos. In some places on Shabbos after prayer is finished the entire congregation accompanies the Chasan home and they say Sheva Berachos, because not everyone was there on Erev Shabbos and now everyone is there. Rav Hai disapproved, but said that it is not forbidden because the Gemara said that we bless Birkas Chasanim all seven days if Panim Chodoshos came. Some say that we bless due to Panim Chodoshos only after a meal. Maseches Sofrim (19:11) says that we bless Birkas Chasanim in the morning over a cup (of wine) with 10 (our text in Maseches Sofrim - and with) Panim Chodoshos all seven days, and also in the evening before the meal. Some say that the 'first day' refers to the first meal. However, even if they did not eat until night, they bless. They are like Panim Chodoshos, for they did not yet eat. Even though we blessed on Shabbos night, we bless Shabbos morning because the honor of the day meal is greater. This is like new Panim Chodoshos.

Ritva (7b DH Omar): Panim Chodoshos are people for whom we increase the Simchah. A woman is not in this category even if she is esteemed, because she cannot join to the 10.

Poskim

Shulchan Aruch (EH 62:7): If others ate who did not hear the Berachos of Nisu'in at the Nisu'in, we bless for them after Birkas ha'Mazon the seven Berachos like we bless at the Nisu'in. This is if there are 10, including the Chasan. Some say that even if they heard the Berachos at the Chupah if they did not eat there until now they are called Panim Chodoshos. This is the custom.

Beis Shmuel (7): The Ran and the Bach say that it suffices to have one new person.

Pischei Teshuvah (14): R. Betzalel says that a woman is not considered Panim Chodoshos, because she cannot join to the 10. Therefore, the same applies to children. If they started with 10 or with Panim Chodoshos but finished without (someone left), they may finish.

Mishneh Halachos (2:47 DH Hineni and 7:246 DH b'Siman): The Chasam Sofer (Kesuvos 7b DH b'Makhelos) says that a woman or child can be Panim Chodoshos if they increase Simchah for her. The Acharonim say not to do so, lest it lead to mixing of men and women.

Yavi'a Omer (3:EH:11 DH Nehader): Here in Eretz Yisrael we follow the Rambam, who requires two new people.

Rema: Some say that if Panim Chodoshos were there, even if they do not eat we bless for them at night and during the day.

Beis Shmuel (9): Most Poskim disagree with this. Therefore, they needed to say that we bless on Shabbos morning because it is the primary Seudah. The Rema himself (below, Sa'if 8) says that we bless at Seudah Shelishis because the Drashah is like Panim Chodoshos. Perhaps here he teaches that Panim Chodoshos permit blessing only at one meal at night and one during the day.

Shulchan Aruch (8): Some say that Panim Chodoshos are only people for whom we increase (Simchah).

Chelkas Mechokek (13): At least they must be people over whom the Bnei Chupah rejoice. Even if they did not increase Simchah for them, it suffices that they are worthy to increase for them. Some say that this is even if they did not eat there.

Shulchan Aruch (ibid.): Some consider Shabbos and Yom Tov Rishon and Sheni to be Panim Chodoshos at the night and morning meals, but not at Seudah Shelishis. This is the custom.

Beis Yosef (DH v'Shabbos): This is because Seudah Shelishis is not as important as the other meals. Some say that one is Yotzei without bread.

Rema: Nowadays the custom is to bless Sheva Berachos also at Seudah Shelishis. Perhaps this is because new people often come. Some say that it is because we normally expound, and this is like Panim Chodoshos.

Beis Yosef (OC 546 DH veha'Rashba): The Rashba (7:9) says that if someone married before Yom Tov and Panim Chodoshos came during the Mo'ed, we do not make a Seudah to bless Sheva Berachos. This is because we do not mix Simchos (Nisu'in and Mo'ed). If they came by themselves perhaps we bless, for a Chasan needs a Berachah when there are Panim Chodoshos. Perhaps we do not Mevatel this due to Simchas Mo'ed.