Tensegrity

Tensegrity, a term coined by one of this century's greatest minds, Buckminster Fuller, is a moniker for tensional integrity, and refers to a type of lightweight construction where tension and compression members are balanced computationally in space with every member being either in pure tension or pure compression. Typically made of lightweight rod and cable systems, the result is often a delicate-looking structure which is actually mathematically as strong as it's component material properties allow. According to Donald Ingber at Harvard:

"The tension-bearing members in these structures – whether Fuller's domes or Snelson's sculptures – map out the shortest paths between adjacent members (and are therefore, by definition, arranged geodesically) Tensional forces naturally transmit themselves over the shortest distance between two points, so the members of a tensegrity structure are precisely positioned to best withstand stress. For this reason, tensegrity structures offer a maximum amount of strength."

When he first saw the sculptures by Kenneth Snelson, Fuller realized the potential of the technology and incorporated the system in the development of his famous geodesic domes.
Fuller was able to observe that the basic priciples of the system were the same:

"Tensegrity is a contraction of tensional integrity structuring. All geodesic domes are tensegrity structures, whether the tension-islanded compression differentiations are visible to the observer or not. Tensegrity geodesic spheres do what they do because they have the properties of hydraulically or pneumatically inflated structures."

Although structurally efficient, for many years the structures were left to sculptures and small scale construction due to it's need for adjustment and the fact that a single structural failure will cripple the system (though that may be part of it's natural beauty). However, with advancements in construction methods and computational modeling, tensegrity structures are again being considered for large scale development and construction. The Kurlipa Bridge in Brisbane, Australia was designed and built on the principles of tensegrity and appears to span the river below with a minimal cross-section.
Filamentosa is a skyscraper envisioned by the firm ORAMBRA that sees a solid core wrapped by a tensegrity structure.
The firm, whose moniker stands for The Office for Robotic Architecture, sees structure like this as an integral component in the future of "smart" buildings. From ORAMBRA:

More than being a series of smart systems attached to a dumb building frame, responsive architectures actually consist of intelligent frames, skins and systems. These buildings change shape and color. They have intelligent systems within them and around them. They track the sun gradually and they adjust their shape to improve shading in the summer or day lighting in the winter. They shake snow from their roof. They even change shape to reduce wind loads or improve the way they ventilate. Unlike the conventional boxes that we live in, these buildings adapt to the natural environment to improve the way that people live. They address suitability and socio-technical issues in three key ways. Firstly they provide a means to reducing the mass and embedded energy used within buildings without sacrificing robustness. Secondly they enable architects to produce a new class of building envelopes that actively adjust and shape themselves in relation to the natural environment, its seasons and weather. With this they offer great potential in reducing the energy used within buildings.

See more examples of tensegrity at oobject.