What’s up with oil prices? Well, it’s not speculators, and there’s no relief in sight, meaning at least five more years of high prices with no easy fixes. The ugly truth? Peak oil isn’t fringe anymore—it’s going mainstream.

That’s the reading from the latest oil market report from the International Energy Agency, the rich-country energy watchdog. The IEA’s latest x-ray of the oil market includes plenty of disturbing nuggets.

The...