Where do dinosaurs fit in with the Bible?

In most cases, there seem to be two thought groups when dealing with the issue of Christianity and dinosaurs.

The first group would be called young-earth creationists. They believe that dinosaurs were created in the same week as humans and therefore coexisted with them on the earth. Most young-earth creationists agree that the dinosaurs then died out at the time of the great flood.

The second group is the old-earth creationists. They take Genesis 1-3 to be an allegorical account of creation and not a scientific one. If this is the case, then each "day" of creation could be seen as a time period of millions of years. They believe that the dinosaurs lived million years ahead of humanity and therefore agree with the majority of paleontologists. While this theory is most relevant with modern-day science, it also comes with numerous theological problems.