For many Eschatology is something that is all about the "end times" of this age. So there are a ton of books and studies out there that try to convince people the proof of different "prophecies" and even to the point of setting dates as to the end of the world. So much of our culture's fetish on the future is fed by Christian and not Christian sources that for many "the End Times" has become a code for determine who among us is "that kind of people".
Here is the rub though, Jesus spoke a lot about the end times. There are many writings and teachings about the eschatological mission of Jesus. Read the Gospels and you will find Jesus speaking of the "end" rather often. To be clear, I am not convinced that Jesus' notion of the "end" is anything that we might consider today. Put another way, it is clear to me the "End Times" of the Left Behind and John Hagee is not what Jesus meant when he spoke of the end.
Realized Eschatology is perhaps closer to what Jesus was getting at in his teaching. The end is here - right now - among us all the time. We just need to look.
When there is peace - Realized Eschatology.
Where there is justice - Realized Eschatology.
Where there is reconciliation - Realized Eschatology.
All of these things happen here and now. Realized Eschatology is what happens when we are able to see the "end" in the present.
You might ask, "How can the end be in the present?"
I would ask, How can the first be last and the last be first? How can Christ be fully God and fully human? How can we live by dying? How can light be a wave and a particle? How can two particles be connected even when they are miles apart?
We live in a world full of paradoxes and "the end is present" is another one to consider.