Here's an interesting talk by Ajahn Amaro, present abbot of Amaravati monastery in England. "The breakthrough" is what he calls stream entry. Here are links to the
talk and to the succeeding
Q&A.
I found these helpful in understanding the perspective of a seasoned Thai forest monk (Ajahn Amaro was a disciple of Ajahns Chah and Sumedho). Not surprisingly, the destruction of the first three fetters are considered the mark of stream entry. He also expounds on what this means in his tradition.