Flexibility is a rather common property of metals, which can be deformed without breaking, but not for ceramics. Often you cannot deform a ceramic by even one percent of its size without it shattering. Researchers at MIT and Singapore though have created flexible ceramics that are also able to remember their original shape.
To make the flexible ceramic, the researchers made it small, but with large grains. Smaller objects are typically more resistant to cracking, and increasing grain size reduces crystal-grain boundaries, where cracks most often form. This combination of techniques allowed the researchers to make a micrometer-wide filament of zirconia that can be deformed up to seven percent its size without breaking. The shape-memory property is something seen in some metals and polymers, but has never been seen in ceramics before, though the mechanics involved would allow it. The issue has been that ceramics would break before the property could be utilized.
The researchers believe the ceramic has potential in micro and nanodevices as an actuator. As the material is able to push things with more force than anything else for its size, the researchers are probably right.