Abstract: In this talk I am going to present one of the most novel structures that has been experimentally observed: supersolids. The supersolid phase is a state of matter that simultaneously presents superfluidity and solid order (by breaking translational invariance). This dual behavior opens the door to many intriguing phenomena both from the static and the dynamic perspective, since supersolids display solid and non dissipative fluid features at the same time.

I am going to provide an overview about what has been found already in the topic of supersolids, paying special attention to excitation of collective modes, the still ongoing studies on the characterization of the superfluidity of a supersolid and the role of the dimensionality and an external confinement.

After that, I will comment about one of the main future perspectives of supersolids: binary dipolar gases.Two-component systems present richer properties, since features such as miscibility and polarization (under the presence of Rabi coupling) play now a crucial role. The possibility to excite independently the density and the spin chanel in a two-component supersolid paves the way to the study of magnetic effects in supersolids and to the eventual nucleation of novel domains.