Much of the following is from Rabbi Pirutinsky's discussion of the subject in Sefer HaBris, starting page 290. He quotes all the Rishonim and Acharonim. I am making it simple through just giving the opinions.
One of the more impactful blessings we have in our liturgy is the "Shehechiyanu"
ברוך אתה ה' א-לקינו מלך העולם שהחיינו וקימנו והגיענו לזמן הזה
Blessed are you Hashem, our God, King of the universe, Who has had us live, and survive, and brought us to this time.
We say this blessing on holidays and other special occasions, mostly when a special event has not happened for over 30 days. (There is an entire Siman in the Shulchan Arukh - Orach Chaim 225 - dedicated to this blessing!)
Do we say it at a bris?
