Would you drink recycled sewage? It’s a question you may need to think about someday.

In recent years, the idea of creating a circular economy—in which all of the resources coming into our cities are recycled after they are used—has taken hold. We now routinely recycle paper, glass and food scraps, as well as parts of demolished buildings and crumbling highways. Widespread sewage recycling could be the next frontier.

Productively...