We have a few "official" fast days:
Tzom Gedalia – The last Jewish administrator killed and the final Jewish community sent into exile
10th of Teves – Siege in the time of the 1st Beis Hamikdash
Taanis Esther - "Only" a long standing custom.
17th of Tammuz – Destruction of the wall of Jerusalem
- 9th of Av – Destruction of the two Batei Hamikdash
Why are there no fast days when the Mishkans were destroyed, when the first group of exiles were sent, or when the Jewish kings became subjugated to Bavel?