We have recently proposed an experiment to cool to the ground state
and create quantum superpositions of the center of mass motion of an
optically levitating nanodielectric.  This can be achieved by exploiting
the coupling between light and the mechanical motion, which is obtained
when the object is trapped inside a high quality optical cavity. I will 
discuss this proposal, its potential applications,different specific 
proposals to prepare and measure quantum superpositions, and the general 
quantum theory that we have developed in order to describe these systems.