Whose Kingdom?

What do the biblical authors mean when they write "Kingdom of God"?  What did Jesus mean when he said "Kingdom of God"?  What would the people understand Jesus to be talking about when he went from town to town saying that the "Kingdom of God" was drawing near?  Heaven?  Or perhaps something more?  Something far more radical and world-changing... a world in which God's sovereign will for peace and mercy is made clear on earth as it is in heaven.  And how does Jesus the Messiah usher in this Kingdom?  By rising up with sword in hand?  No, he mounts a cross and pours out his life.