Celebration of Bar & Bat Mitzvah

In the past

The Bible makes no mention of a Bar Mitzvah ceremony or celebration, but it is clear that the custom was common towards the end of the Second Temple period, as can be learned from ancient texts.
The Sages anchored the custom in the Bible by applying various homiletic commentaries to events in the Bible.

According to Midrash Genesis Rabba (53, 10) Abraham held a feast when Isaac was "weaned" (Genesis 21, 8) away from the evil inclination and was ready to accept the responsibility of the Commandments.
Elsewhere, Midrash Genesis Rabba (63, 10) explains that Jacob "grew" (Genesis 25, 27) and then went to Bet Hamidrash (to study Jewish law).

According to Masseket Sopherim (18, 11) in the Talmud, after being trained, a mature boy was brought before the priest or elder to be blessed and encouraged to learn the Law and obey it. That would include the right to be called up to read a portion of the Torah.

The first report of an actual Bar Mitzvah ceremony seems to be that of the son of Rabbi Yehudai Ga'on. The Rabbi is reported to have said that he had recited, in the synagogue, the blessing thanking G-d for removing the burden of responsibility for his son's sins when the son was called up to read the Torah for the first time (Orhot Hayyim, Berakot, 58).

Rabbi Abigdor Hatzarfati (13th century) ruled that a religious feast should be held to celebrate a boy's thirteenth birthday (Perushim UPsakim al HaTorah, 4 [8]).
Rabbi Menahem Tziyyoni (15th century) seems to be the first person to use the term “Bar Mitzvah” to mean the occasion of becoming obligated to obey the commandments (Sefer Tziyyoni, comment on Genesis 1, 5).
Rabbi Shlomo Luria (“Maharshal”, 16th century, Poland) observed that the Jews of Ashkenaz (= Germany) would celebrate the Bar Mitzvah with a religious feast where a sermon would be delivered, probably one the youth had prepared (Yam Shel Shlomo, Baba Kama, 7:37).
The Book of Customs of the Worms Community (Germany, mid-17th century) notes that being called up to read from the Torah was a central part of the Bar Mitzvah ceremony there (Peraqim LeToldot HaHinnukh BeYisrael, vol. 1, 108).
Rabbi Abraham Gombiner (17th century, Poland) ruled that a religious feast celebrating a Bar Mitzvah should be as elaborate as if the youth were marrying (Magen Abraham, Orah Hayyim, 224, 4).

A common topic for the sermon would concern Tefillin and it was often called Drashat Tefillin or Drush Tefillin. Among the Jews of Morocco it was common, at least from the beginning of the 19th century, to celebrate the Bar Mitzvah with a feast on a Wednesday, when the boy would wear Tefillin and deliver a sermon; he was consequently called up to read from the Torah on the coming Shabbat.  
In Tangier in northern Morocco, the Bar Mitzvah sermon was already the central part of the ceremony in the 17th century.
Among the Jews of Iraq, too, the ceremony had these two stages. There, during the service, the celebrant's younger brothers would show their respect for him by rising and standing from the moment he was called up till he returned to his seat (MiMinhageyhem Shel Yehudei Iraq 24-30).
The custom in Persia was similar: on one of the days on which the Torah was read, the young celebrant would put on Tefillin and then be called up to the Torah, accompanied by the congregation’s singing in his honor and their showering him with candies. A religious feast at his house followed. On the following Shabbat, the youth was called up to the Torah in a similar fashion, after which the family offered candies and sweetmeats to the congregation. A feast for the extended family ensued.
In the Yemen, however, the Bar Mitzvah boy’s sermon was the climax of the ceremony, as there younger boys were also called up to read from the Torah.

The existence of a special religious celebration of a Bat Mitzvah for a girl is known only since after the early 19th century in Germany and in Italy (Efrati, BiSdeh Hemed 1961; Zebed HaBat; Barkat, Haaretz newspaper, May 27, 2003).
In Germany, Rabbi Ettlinger would deliver an address at such celebrations in the mid-19th century.
In Iraq it was strongly advocated by Rabbi Joseph Hayyim (Ben Ish Hai, 1st year, "Re'eh", 17) but did not carry a formal religious characteristic.

The first time a girl was called up to read from the Torah as part of becoming a Bat Mitzvah was in the early 1920s (Barkat). Several rabbis of the 20th–21st century have voiced the opinion that a girl’s Bat Mitzvah should be celebrated or even followed up on this by specific actions.
In Tunis, Rabbi Shetroug used to deliver a sermon during girls’ Bat Mitzvah celebrations during the 1920s.

After the Holocaust, Rabbi Yehiel Weinberg wrote that he thought it logical and almost obligatory to celebrate a girl’s Bat Mitzvah (Seridei Esh 2, 39).
Rabbi Meshulam Ratta (Roth) wrote, in 1957, that he supported celebrating a girl’s Bat Mitzvah (Kol Mevasser 2, 44).
Rabbi Hanokh Grosberg published his opinion that a girl’s Bat Mitzvah was to be celebrated within the family, accompanied by a sermon on girls’ education, thereby turning the occasion into a religious feast (HaMa’ayan 1962).
Rabbi Yitzhak Nissim, (in 1963) said a girl’s Bat Mitzvah is to be marked by her praying in the synagogue, and celebrated at a  feast in honor of the occasion at which she delivers a sermon and reads out Judges 5, and her father pronounces he is no longer responsible for her sins. This turns it into a religious feast and all those invited are obligated to participate.
Rabbi Musafia said that a father’s feast in honor of his daughter having reached the age she is obligated to fulfill the commandments is worthy of being a religious feast.
Rabbi Ovadiah Hadayah says that as at Bat Mitzvah a girl becomes a young (obligated) woman, she has reached a higher personal level and therefore deserves a religious celebration.
Rabbi Ovadiah Yosef, relying on several of these modern predecessors, complains about the discrimination between boys and girls reaching the obligatory age, and says a girl’s Bat Mitzvah should be celebrated (Yabia Omer, part 6, 15).

Nowadays

Today the most basic form of a Bar Mitzvah ceremony is the celebrant's first Aliyah laTorah (calling up to read from the Torah). On the Shabbat, Monday or Thursday morning service after the child's thirteenth birthday, the celebrant is called up to the Torah to recite the blessings preceding and following the reading of one part of that week’s Parashah.

It is common practice for the Bar Mitzvah celebrant to do much more than just recite the blessings. Usually the celebrant also learns the entire Haphtarah, including its traditional chant, and recites that. In some congregations, the celebrant reads the entire weekly Torah portion, or leads part of the service, or leads the congregation in certain prayers.
The celebrant may sometimes also be required to deliver a sermon. The father recites a blessing thanking G-d for removing the burden of responsibility for the son's sins.
The religious service is often immediately followed by a ritual meal in the synagogue for the congregants, at which the Bar Mitzvah may be the adult to recite Kiddush (brief prayer and blessing preceding the meal).

Rituals are usually complemented by a party that is often as elaborate as a wedding reception.
Family, friends and members of the synagogue come to celebrate the young person’s coming of age. The Bar Mitzvah or Bat Mitzvah actively participates in the ceremonial parts of the reception party, reading prayers and making a personal speech, which traditionally begins with the phrase "Today I am a man."
In some communities it is still the custom for the audience to start singing loudly a short while after the speech begins, thereby cutting the sermon short. This is done so that the young Bar Mitzvah wouldn't feel embarrassed if he couldn't proceed with the sermon due to stage fright.

The precise form of a girl's Bat Mitzvah ceremony varies, depending on the branch of Judaism and the young adult.
In some congregations it is exactly the same as a boy’s Bar Mitzvah. In others, the Bat Mitzvah may read from the Torah after the regular reading (in the women’s partition or in front of the Ark), during or immediately following the general service.
In some congregations the Bat Mitzvah may deliver a sermon during a special mixed or an all-female service or religious feast.
The sermon traditionally focuses on the religious aspects of becoming an adult woman, such as lighting candles, preparing challah, religious physical purity, children’s education, or any religious topic stemming from the week’s Portion.
Sometimes the young adult reads the Song of Songs. 
In other communities the Bat Mitzvah’s sermon may include religious learning, praying in front of the Holy Ark, and even reading from the Torah.
In some cases the girl’s father is called up to the Torah in the synagogue.
According to the above-mentioned modern rabbis, he may then recite the blessing thanking G-d for removing his responsibility for the daughter’s sins.  In other cases he gives a Talmudic lesson in his daughter’s honor.

In ultra-orthodox and Hasidic practice, women are present but not active participants in religious services in the ways outlined here, so a Bat Mitzvah celebration, if marked at all, may be little more than an occasion for a new dress and a family party.

Some Jewish boys and girls may not have a formal ceremony at all. However, their religious obligations do not depend on any ceremony, but on having reached the right age.

See also:
- Meaning of "Bar Mitzvah"
- The Right Age for Bar & Bat Mitzvah
- Sources