Emperors are the leaders of Elysium's nine capital cities, and by extension the leaders of the racial empires based out of them.
As the head of a cities government, the Emperor is responsible for appointing the Ministers who will run the city, and can on occasions seize powers of those ministries to get things done. The Emperor also has some direct powers.
In addition to these powers, Emperors can also hold court and hear petitioners from their citizens.
Although they can all be referred to as Emperors or Empresses, in different cities the position may be styled differently, and rulers using the titles of King or Queen are not uncommon.