Complementarians believe that men and women are equal but have different yet complementary roles assigned by God.
What do complementarian church leaders in history believe are the differing roles of men and women in the church?
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There are two principal kinds of church that have 'complementarian' doctrines.
In the first case there are churches with ordained clergy that reserve the office of Priest for men. Chief among these is the Roman Catholic church, but there are others. The priestly role includes celebrating the Eucharist (Mass), and church leadership.
Not all churches with ordained clergy reserve the office of Priest for men. Those that do also reserve higher offices such as Bishop. Some churches are in transition, allowing women to be Priests but not Bishops, for example.
The second kind of complementarians are generally Evangelical Protestants. They can have very varied doctrines, but they almost invariably also reserve certain church roles for men, and those roles are centred around leadership, authority and teaching.
Example restrictions might be any or all of:
Again, not all Evangelical Protestant churches reserve some roles to men.
I know of no church which reserves any roles for women as a matter of doctrine.