There are two major fast days - Yom Kippur and Tisha B'Av. 

There are five minor fasts on the Jewish calendar. With one exception, these fasts were instituted by the Sages to commemorate some national tragedy.  On the minor fasts, one is permitted to eat breakfast if one arises before sunrise for the purpose of doing so. There is a great deal of leniency in the minor fasts for people who have medical conditions or other difficulties fasting. The date of the fast is moved to Sunday if the specified date falls on Shabbat. 
 The Fast of Gedaliah,

Tishri 3, commemorates the killing of the Jewish governor of Judah, a critical event in the downfall of the first commonwealth.

 The Fast of Tevet, Tevet 10, is the beginning of the siege of Jerusalem. It has also been proclaimed a memorial day for the six million Jews who died in the Holocaust.

The Fast of Esther, Adar 13, commemorates the three days that Esther fasted before approaching King Ahasuerus on behalf of the Jewish people before Purim.  


The Fast of the Firstborn, Nissan 14, is a fast observed only by firstborn males, commemorating the fact that they were saved from the plague of the firstborn in Egypt. 


The Fast of Tammuz, Tammuz 17, the date the walls of Jerusalem were breached.

 New holidays:
 Yom Ha-Shoah. 

This holiday, also known as Holocaust Memorial Day, occurs on the 27th of Nissan. "Shoah" is the Hebrew word for the Holocaust. This is a memorial day for those who died in the Holocaust.

Yom Ha-Zikkaron. 

 Israeli Memorial Day, observed on Iyar 4, remembers those who died in the War of Liberation and other wars in Israel.


Yom Ha-Atzmaut. 

Israeli Independence Day, marking the establishment of the modern state of Israel in 1948. It is observed on the 5th of Iyar. 

Yom Yerushalayim.  The 28th day of Iyar commemorates the reunification of the city of Jerusalem in Israeli hands.