As far as I can discover, I don't think there is a "Caliphate" yet. I think the Islamic "messiah" has to return, plus a unified muslim empire of all the faithful must exist, before a Caliph can be appointed, or elected, or however he is picked to assume command of the world's muslims. And by the way, it will be a "he".
A caliphate does not require the Return or a Messiah. It is a system of government that had a fairly long history in the past. Those who desire the caliphate either simply believe that a caliphate is the only proper form of society and/or they believe that establishment of the Caliphate is part of the conditions necessary for the Return. Paradoxically it is the Shiites who are most invested in the concept of The Return or a Moslem Messiah. The Sunnis have their own version but it is not quite the overriding cause of everything as is with the Shia.