Today is 10 Tevet 5772, the minor fast day known as the 10th of Tevet. On this day (literally, which as we shall see is important) 2,436 years ago, in 425 BCE, King Nebuchadnezzar of Babylon began the siege of Jerusalem that, two and a half years later, led to the destruction of the First Temple (on Tisha B’Av). “And it came to pass in the ninth year of his reign, in the tenth month, in the tenth day of the month, that Nebuchadnezzar king of Babylon came, he and all his army, against Jerusalem, and encamped against it; and they built forts against it round about,” reads the first verse of the final chapter of II Kings. This, in turn, was followed by the Babylonian exile. So, it’s really the beginning of everything going downhill.

In honor and recognition of which, should you choose to observe the day, you should refrain from food and drink from sunrise to sunset (or, if you prefer, from Daybreak to Sundown). And indeed the 10th of Tevet, say some, should always be observed on, well, the 10th day of Tevet, because a phrase in Ezekiel suggests that this really is the exact day that the events it commemorates occurred. That means if the holiday falls on Shabbat, as it will in December 2013, then you observe it then; the only other fast day of which this is true is Yom Kippur. (As with all fasts, the ill, the elderly, the infirm, or the pregnant or nursing are exempt from fasting requirements.)

In recent years, many have looked upon the 10th of Tevet and its message of sorrow and utilized it as a day to remember the victims of the Holocaust. Indeed, since Yom HaShoah comes in Nisan, during which mourning is supposed to be prohibited, observant Jews tend to prefer today for remembering the 6 million.

Tenth of Tevet [Wikipedia]
10 Tevet [Chabad]