In 1941, the Swiss inventor George de Mestral went on a hunting trip. Along the way, burdock burrs stuck to his pants and to the fur of his dog. Curious about their power to cling, de Mestral put the burrs under a microscope. He saw thousands of tiny hooks. The sight led him to imagine a new kind of fastener, one that wouldn’t rely on knots or glue.

A few years later, de Mestral discovered a substance that could make that idea real: nylon. The synthetic fiber could be permanently bent into a hook. De Mestral found that nylon hooks readily attached to fabric and could be peeled away. In 1955, he filed a patent for his invention, which he called Velcro, a combination of the French words “velour” (“velvet”) and “crochet” (“hooks”).

When engineers in Japan created a fleet of high-speed trains in the 1980s and 1990s, they also created some unexpected problems. A train traveling through a tunnel faster than 220 miles an hour compressed the air ahead of it. When the pressure wave reached the tunnel exit, it created a sonic boom.

An engineer named Eiji Nakatsu cast about for a way to make the trains quiet. “The question then occurred to me — is there some living thing that manages sudden changes in air resistance as a part of daily life?” Mr. Nakatsu recalled in a 2005 interview.

Mr. Nakatsu was not just an engineer, but also an avid birder. As he pondered the question, the kingfisher came to mind. When the bird dives at high speed to catch fish, its beak slips into the water without a splash.

So Mr. Nakatsu and his colleagues built train engines with rounded, tapered front ends. Their kingfisher-beak shape reduced the air pressure in tunnels by 30 percent, making the trains quieter and more efficient, even as they traveled more rapidly through tunnels.

In the 1990s, Frank Fish took a close look at the massive knobs that stud the leading edge of humpback whale fins. Dr. Fish, a biologist at West Chester University in Pennsylvania, and his colleagues discovered that these tubercles significantly improve the whales’ performance by keeping water flowing smoothly over their fins, generating extra lift.

Dr. Fish and his colleagues patented their discovery, which has since been adopted by engineers to improve a long list of devices. Tubercles extend the life span of wind turbine blades, for example, and make industrial ceiling fans more efficient. They can even be found on surfboard fins and truck mirrors.

A gecko’s foot is covered by a half-million tiny hairs, each of which splits into hundreds of branches. When a gecko slaps its foot on a wall, many of the branches push tightly against the surface. Each branch creates a weak molecular attraction to the wall, and together they generate a powerful force, yet the gecko can easily pull its foot away in a millisecond.

Dr. Irschick and his colleagues created a fabric that mimics these forces, which they called Geckskin. A piece the size of an index card can hold 700 pounds to a glass surface and be moved without leaving a trace behind.

Pitcher plants are carnivorous, feeding on insects that crawl onto the rim of their pitcher-shaped leaves. The rim is exquisitely slippery, causing prey to lose their footing and fall into a pool of digestive enzymes.

Researchers discovered that when rain and dew collect on the plant, microscopic bumps and ridges pull the water into a film that sticks to the legs of insects. The bugs struggle for traction and end up swimming — and falling.

In 2011, Joanna Aizenberg, an engineer at Harvard, and her colleagues created materials with pitcher-plant patterns on their surface, and these turned out to be slippery as well. A company co-founded by Dr. Aizenberg sells coatings that keep sticky fluids from clogging pipes and paints that repel barnacles from ship hulls.

The mantis shrimp has a pair of odd limbs called dactyl clubs that look a bit like boxing gloves. It uses the clubs to deliver staggering punches with a force equal to that of a .22 caliber bullet — enough to crack open shells. Scientists have long wondered why those impacts don’t crack the dactyl club itself.

Through evolution, the mantis shrimp gained an exoskeleton of astonishing complexity. Its dactyl clubs are composed of layers of fibers; some form herringbone patterns, while others are made of corkscrew-like bundles. These layers deflect the energy from a punch, preventing it from spreading and causing damage.

In May, researchers at the National Institute of Standards and Technology reported the creation of an artificial version of these shock-absorbing layers. When microscopic beads of silica were fired at the material at 1,000 miles an hour, it dented but did not crack. The researchers foresee using the material to make lightweight shields for spacecraft, to protect them from tiny meteoroids.

Ripple bugs are about the size of a grain of rice. They float on the surface of streams by spreading out their legs across the water — but they can also move with astonishing speed, roughly 120 body lengths each second. At a human scale, that would translate to 400 miles an hour.

The secret lies at the end of the middle pair of legs. When a ripple bug dips them into the water, surface tension causes stiff fronds at the ends to fan out in just 10 milliseconds, and the fans become oars. At the end of each stroke, when the insect lifts these oars from the water, the fans snap shut.

In August, Victor Ortega-Jiménez, a biologist at the University of California, Berkeley, and his team announced that, following these principles, it had built tiny robots that walk on water, make rapid turns and brake sharply. And because the water forces the fans open and closed, the Rhagabots — after Rhagovelia, the Latin name for ripple bugs — require little energy from their onboard batteries.

The paralyzing blasts of electricity that an electric eel delivers arise from a sleeve of tissue that wraps around the animal’s body. The tissue contains thousands of layers of cells, which are sandwiched in turn between layers of fluid. The cells pump charged atoms into the fluid, creating a biological battery.

Michael Mayer, a biophysicist at the University of Fribourg in Switzerland, and his colleagues are working to mimic the electric organs in electric eels and other fish. A biologically inspired battery could offer big advantages over conventional ones. They could be safer sources of power for medical implants, for instance, because they would run on organic compounds rather than toxic chemicals.

The team has built contact-lens-shaped prototypes from soft, bendable gels. Dr. Mayer hopes one day to implant the batteries with the same proteins that electric eels use to move charged atoms around.

“Building all this so that it really does the same thing as in the fish is right now beyond our reach,” Dr. Mayer said. “I think this is far in the future, but the project has already gone much further I thought it would.”