What happens if you don't found a religion?

Suppose the other civilizations have founded all the religions that could be founded in that map (that never happened to me, but I'm curious, but not curious enough to spend a night doing an experiment).

So what happens to you? Do you play without the bonuses of a religion? How do your religious units work? E.g. could you convert citizens to atheism with a missionary?

If you do not found a Religion, you can still enjoy the Follower Beliefs of one of the AI's religions. Over time, either natural pressure or AI Missionaries/Great Prophets may spread a religion to your cities, at which point you may benefit from whatever Follower Beliefs the religion carries, as well as the Enhancer beliefs if they are relevant to you and to the selected Follower beliefs. You do not gain the ability to purchase Missionaries unless the city is religious in some way, however (and no, a Pantheon does not count).

Note that this does not preclude you from being able to purchase Great People with Faith as dictated by your Social Policy choices. You do not need an active religion in a city to acquire a Great Merchant while Mercantilism is active, for example.