While time crystals remain theoretical, methods have been proposed for creating them. The most obvious application of time crystals is the creation of very precise clocks; however, other applications to time crystals have been proposed, ranging from quantum computing to helping us understand certain cosmological models.
A technical summary with links to the original publications can be found at: http://physics.aps.org/articles/v5/116
For a less technical summary: http://www.scientificamerican.com/article.cfm?id=time-crystals-could-be-legitimate-form-perpetual-motion
Link to Original Source