Caesaropapism and theocracy represent two different systems. Caesaropapism is a system in which the state also governs religious matters. The Byzantine Empire is one of the well known examples of the early form of caesaropapism. After one Byzantine emperor gradually tightened his control over religious affairs, his successors all acted as custodians of the Church and the appointment of the archbishop of Constantinople had to be first approved by the emperor. As it is a system in which the state holds power over religious matters, some people argue that China also runs a type of caesaropapism based on secularism, except that religious institutions do not meddle with private life.
There are cases where the head of state grants more power to a certain religious institution and thus facilitates shadow caesaropapism, despite the clear mandate of separation of church and state.
So what about the other way around when the church interferes with political affairs? The most extreme case would be a theocracy where the state is led by a religious leader. The remaining theocracies of our times include the Holy See (Vatican City State) and Islamic Saudi Arabia and Iran.
- The Holy See (Vatican City State): The head of state is Pope Francis.
- Saudi Arabia: The head of state is the King of Saudi Arabia and he is also the Custodian of the Two Holy Mosques.
- Iran: The president is only the nominal head of state. Ali Khamenei, the supreme religious leader, is the one with actual ruling power.