nothing happened to it ,basically they are christian living with Muslims sharing the same culture ,they didn't change but they live in the same countries so they go by the culture which is now their culture since they were there be for Muslims.they don't dress up like Muslims (head cover except during service optional)
They got treated according to the rules of Islam: tolerance, but as second class citizens. They had to pay a special tax, not ride horses, not use church bells, a Christian had to convert if he wanted to marry a Muslim, etc.
depending on which orthodox church you talk about..
the Greek orthodox one flourished because the Turk were incredibly tolerant in the beginning.. much more so than any other nation in Europe (i am Greek.. believe it pains me to admit this).. on the other hand smaller churches such as the Bulgarian orthodox and Serbian church were borough under the jurisdiction of the Greek episcopate.. so from their perspective they were suppressed.
The caliph made the Ecumenical Patriarch responsible for keeping the Orthodox people in line.
Many Orthodox apostatized and converted to Islam to avoid paying taxes and oppressed their fellow citizens. Look at Kosovo as a reminder.
Wealthy ex-patriot Greeks funded secret schools where priests taught the language and culture under the cover of darkness. In 1821, a Bishop declared Greek Independence.
Otherwise, the church functioned as usual because the Ottomans were tolerant of "peoples of the book."