We discuss our recent research advances about wave control and manipulation using periodic temporalmodulation of a system’s properties. By using the unique properties of time-Floquet systems, we constructacoustic metamaterials with extreme effective properties, such as zero index of refraction. Furthermore, theinteraction with a periodic drive can lead to power exchange with the wave, providing a unique route to non-Hermiticity. We demonstrate non-Hermitian acoustic systems based on time modulation, such as Parity-Timesymmetric parametric amplifiers.