Researchers in the US and Britain have unveiled their blueprints for building a cloaking device.
So far, cloaking has been confined to science fiction; in Star Trek it is used to render spacecraft invisible.
Professor Sir John Pendry says a simple demonstration model that could work for radar might be possible within 18 months' time.
Two separate teams, including Professor Pendry's, have outlined ways to cloak objects in the journal Science.
These research papers present the maths required to verify that the concept could work. But developing an invisibility cloak is likely to pose significant challenges.
Both groups propose methods using the unusual properties of so-called "metamaterials" to build a cloak.
These metamaterials can be designed to induce a desired change in the direction of electromagnetic waves, such as light. This is done by tinkering with the nano-scale structure of the metamaterial, not by altering its chemistry.
John Pendry's team suggest that by enveloping an object in a metamaterial cloak, light waves can be made to flow around the object in the same way that water would do so.
"Water behaves a little differently to light. If you put a pencil in water that's moving, the water naturally flows around the pencil. When it gets to the other side, the water closes up," Professor Pendry told the BBC.
Special materials could make light "flow" around an object like water
"A little way downstream, you'd never know that you'd put a pencil in the water - it's flowing smoothly again.
"Light doesn't do that of course, it hits the pencil and scatters. So you want to put a coating around the pencil that allows light to flow around it like water, in a nice, curved way."
The work provides a mathematical "recipe" for bending light waves in such a way as to achieve a desired cloaking effect.
John Pendry, along with colleagues David Smith and David Schurig at Duke University in North Carolina, US, have been testing suitable metamaterials for the device they plan to build.
This, Sir John explained, would consist of a sphere or cylinder wrapped in a sheath of metamaterial which could cloak it from radio waves.
"It's not tremendously fancy, but that for us would be quite an achievement," he told the BBC News website.
Professor Ulf Leonhardt, author of another cloaking paper in Science, described the effect for light as a "mirage".
"What you're trying to do is guide light around an object, but the art is to bend it such that it leaves the object in precisely the same way that it initially hits it. You have the illusion that there is nothing there," he told the BBC's Science in Action programme.
The work could have uses in military stealth technology - but engineers have not yet created the materials that could be used to cloak an aircraft or a tank, John Pendry explains. Professor Pendry's research has been supported by the US Defense Advanced Research Projects Agency (Darpa).
Several other scientific teams have proposed ideas for cloaking devices. One theoretical paper proposed using a material known as a superlens to cancel out light being scattered from an object.