10 Tevet 5777
“And it was in the ninth year of his reign, in the tenth month, in the tenth (day) of the month, that Nebuchadnetzar, King of Babylon came, he and all his hosts, upon Yerushalayim, and he encamped upon it and built forts around it. And the city came under siege till the eleventh year of King Tzidkiyahu. On the ninth of the month famine was intense in the city, the people had no bread, and the city was breached.” (Second Melachim 25)
...the tenth of Tevet — on which the siege of Yerushalayim began, was the beginning of the whole chain of calamities which finally ended with the destruction of the Beit Hamikdash.
'The essential significance of the fast of the Tenth of Tevet, as well as that of the other fast days, is not primarily the grief and mourning which they evoke. Their aim is rather to awaken the hearts towards repentance; to recall to us, both the evil deeds of our fathers, and our own evil deeds, which caused anguish to befall both them and us and thereby to cause us to return towards the good. As it is said: “And they shall confess their transgressions and the transgressions of their fathers.” (Vayikra 26. Rambam Hilchot Ta'anit Chapter 5). The aim of fasting, therefore, is to subjugate our evil inclination by restriction of pleasure; to open our hearts and stir us to repentance and good deeds through which the gates of Divine mercy might be opened for us. (Source)