The Four Minor Fasts
Four daylight fast days frame the Jewish year with grief and remembrance.
Summary. In addition to Yom Kippur (the major Torah-commanded fast) and Tisha B'Av (the major rabbinically-commanded fast), four minor fasts are observed annually, three of them connected to the destruction of Jerusalem and the Temple. They are: Tzom Gedaliah (3 Tishrei, the assassination of Gedaliah ben Achikam, the Babylonian-appointed Jewish governor of Judah after the Temple's destruction); the 10th of Tevet (the beginning of Nebuchadnezzar's siege of Jerusalem); the 17th of Tammuz (the breach of Jerusalem's walls); and the Fast of Esther (13 Adar). The minor fasts run only from dawn to nightfall and have lighter restrictions than Yom Kippur or Tisha B'Av.
What Defines a 'Minor' Fast
The four minor fasts are dawn-to-nightfall daylight fasts. They prohibit eating and drinking but not the other inuyim (washing, anointing, marital relations, leather shoes). The synagogue service adds the Avinu Malkeinu prayer and additional readings. Pregnant and nursing women, children, and the ill are exempt. The healthy adult population observes.
Tzom Gedaliah (3 Tishrei)
The day after Rosh Hashanah, commemorating the assassination of Gedaliah ben Achikam in 582 BCE (Yirmiyahu 41, Melachim II 25:25). Gedaliah was the Jewish governor appointed by Nebuchadnezzar over the remnant of Judah after the destruction of the First Temple. His assassination by Yishmael ben Netanyah ended the limited self-government Babylon had allowed the remnant in Judah — though not Jewish political life in the Land for good. The exiles who returned rebuilt under Persian rule with only token autonomy in a subject province; full sovereignty came again only with the Hasmoneans in the second century BCE, and after Rome ended it nearly 2,000 years passed until 1948.
10th of Tevet
Commemorates the beginning of Nebuchadnezzar's siege of Jerusalem in 588 BCE (Melachim II 25:1; Yirmiyahu 52:4). In Israel, the 10th of Tevet is also the date of the Yom HaKaddish HaKlali — the date set by the Chief Rabbinate for the recitation of Kaddish for Holocaust victims whose date of death is unknown. The fast and the modern commemoration overlap.
17th of Tammuz
Commemorates several catastrophes that occurred on this date: the breaking of the tablets by Moshe when he descended Sinai and saw the golden calf (Shemot 32); the cessation of the daily Tamid offering during the siege of Jerusalem; the breach of Jerusalem's walls by the Romans in 70 CE (Mishnah Ta'anit 4:6; the earlier Babylonian breach at Yirmiyahu 39:2 fell on the 9th of Tammuz); the burning of a Torah scroll by Apostomus; the placing of an idol in the Temple. The 17th of Tammuz begins the Three Weeks of mourning that culminate in Tisha B'Av.
Fast of Esther (13 Adar)
The day before Purim, commemorating Esther's fast before approaching the king (Esther 4:16). The Fast of Esther is unique among the minor fasts in not being connected to the destruction of the Temple; it is the only one with a happy aftermath (the joy of Purim follows the next day). Where Purim falls on Sunday, the fast is moved to the previous Thursday (since fasts are not held on Friday afternoon or Erev Shabbat).
Where Denominations Diverge
Orthodox observance of all four minor fasts is universal. Conservative observance is substantial, especially of the 17th of Tammuz and 10th of Tevet. Reform observance of the minor fasts is variable; many Reform congregations do not observe them. The major fasts (Yom Kippur and Tisha B'Av) are more widely observed across denominations than the minor fasts.
Sources
Zechariah 8:19 — "the fast of the fourth, the fast of the fifth, the fast of the seventh, and the fast of the tenth shall be to the house of Yehudah occasions for joy and gladness."
Mishnah, Ta'anit 2:10; Rosh Hashanah 1:3.
Talmud Bavli, Rosh Hashanah 18a–19a.
Rambam, Mishneh Torah, Hilchot Ta'aniyot 5.
Shulchan Aruch, Orach Chaim 549–550, 686.
Jewish Fast Days: What They Are and How to Observe Them — Rabbinical Assembly.
Jewish Fast Days FAQ - The Fast of Gedaliah, 10 Tevet, Fast of Esther, and 17 Tammuz — Chabad.org.
17th of Tammuz — Aish.
Gedaliah in the Bible - Learn 10 Facts About the Leader of Judea Killed in a Betrayal — Chabad.org.
Further Reading
Yitz Greenberg, The Jewish Way — fast days chapters.
Aaron Rakeffet-Rothkoff (Yeshiva University) lectures on the Three Weeks.