In 1956 psychologist J. P. Guilford coined the term “divergent thinking” to describe a thought process that generates out-of-the-box ideas and innovations. It's used by individuals who create surprising solutions to problems that no one else considers. This kind of thinking fills the following pages—the most far-out ideas to tackle some of our biggest challenges, from climate change and water availability to species extinction and debilitating human disease. These atypical, and sometimes controversial, scientific endeavors employ unusual approaches that seem far-fetched but may just save the day.

Take some of these whiz-bang solutions for sustainable living. Rebuilt swamps and waterways in the middle of so-called sponge cities can absorb excess rainfall and clean urban water caches. Solar-powered panels can pull water directly out of the air for human use, and technology that mimics photosynthesis in a leaf can produce fuels to power cars and homes. Even more strange, perhaps, is that we may need to look to the sky to spot early warning signs of impending earthquakes).

As humans alter the planet, other forms of life have to keep up, but some out-of-the-ordinary experiments may help. Several research groups are developing tools to accelerate gene flow in plants and animals, to create varietals of trees and corals that can adapt to their changing environments. Genetic manipulation could also finally mean control over invasive species in the Galápagos that are wreaking havoc on native flora and fauna—or we could just eat them into submission.

Unconventional lines of inquiry are also at the core of the latest advances in human health. Researchers are using a CRISPR recording device programmed into bacterial cells to track everything from infections in the body to elevated pollutant levels in water sources. And what if electrical stimulations administered directly to the vagus nerve could treat a handful of chronic conditions better than any drug? An engineered and fluorescent version of the rabies virus is lighting up neuropathways for study, while lab-grown brains are revealing the origin of disorders from autism to Alzheimer's disease.

Human ingenuity keeps pushing innovation forward, far beyond what was imagined even a few years ago. The challenges we face today feed the machine of creative science on which hangs the sign: Wild Ideas Welcome.