Imagine what it must have been like to look through the first telescopes or the first microscopes, or to see the bottom of the sea as clearly as if the water were gin. This is how students of human prehistory are starting to feel, thanks to a new ability to study ancient DNA extracted from bodies and bones in archaeological sites.

Low-cost, high-throughput DNA sequencing—a technique in which millions of DNA base-pairs are automatically read in parallel—appeared on the scene less than a decade ago. It has already transformed...