| Abstract: | Photonic Time Crystals (PTCs) are dielectric media whose refractive index is strongly modulated periodically in time at time scales of a single optical cycle. These systems conserve momentum but not energy and are characterized by momentum bands separated by gaps where the amplitudes of their eigenmodes increases (or decreases) exponentially. The fundamentals of PTCs will be introduced along with the classical and quantum features of light-matter interactions in them. Among these, the most notable is the emission of light in PTCs, which opens new avenues for making widely tunable lasers that do not rely on any atomic resonance and draw their energy from the temporal modulation of the medium. Finally, I will discuss recent experimental progress on nonlinear optics in such time-varying media. |