For Whom Did Christ Die?

For whom did Christ die---for the world, for Christians, or for both?
In other words, did Christ offer up Himself as a sacrifice for the whole human race, for every individual without distinction or exception? Or did He die, specifically, for some, but not all. The question is important, because how we answer it reveals much about our understanding of the atonement, and God is most glorified when His people have a clear view of the person and work of Christ.