By 2050, the United Nations predicts that over two-thirds of the world’s population will live in urban areas. To many architects, the most appealing response to this this influx is to build vertically. But rather than continuing to colonize the sky by erecting skyscrapers which, as they grow taller, embody ever-louder expressions of bravado, why not consider constructing in the opposite direction?

The idea of going underground is gaining favor. In Mexico City, for example, architecture firm BNKR Arquitectura has proposed a 65-story inverted pyramid—the “Earthscraper”; this nod to the city’s Aztec history could house 5,000 people underneath the Plaza de la Constitución. Singapore and other Asian metropolises have also begun subterranean exploration in response to population bo...