What are all of the emergency triggers?

Solution 1:

According to the Civilopedia there are currently five emergencies,

1. Military Emergency - A civilization that is leading in some victory type has just conquered another's city.
2. City-State Emergency - A civilization has captured and is occupying a city-state.
3. Religious Emergency - A civilization has converted the Holy City of another religion through a religious spread action.
4. Nuclear Emergency - A civilization has used a nuclear weapon on a city.
5. Betrayal Emergency - A civilization has declared war on another civilization with whom they had a high-level alliance.

Participation is based on their diplomatic relationship with the target (person who triggered it). In most of the emergencies the goal has to do with capturing the triggering civilization's cities. The city-state one is to liberate that city-state and the religious one is to convert that holy city to a different religion in time.