In this talk I will review the state of the art and the new perspectives in the theoretical and experimental study of analog models of quantum field theories in flat, curved, or time-dependent backgrounds using condensed matter and optical systems. After a brief presentation of the theory and experiments on Hawking emission of phonons from acoustic horizons in quantum fluids of ultracold atoms and of light, I will present recent results (in collaboration with Luca Giacomelli) on superradiance effects in different geometries. In rotating configurations, the instability of multiply charged vortices can be understood in terms of an ergoregion instability at the vortex core. Introduction of synthetic gauge fields in planar geometries extends the range of space-time metrics that can be generated and allows for analytical insight into superradiant scattering processes. The relation between superradiant scattering and superradiant instabilities will be clarified. As a further extension of the analog model paradigm, I will present how impurity atoms in an atomic fluid can form two-level emitters coupled to the quantum field. Based on recent works with Jamir Marino, Gabriel Menezes and Alessio Recati, I will present observable predictions of Ginzburg radiation and superradiant lasing for moving emitters along linear or circular trajectories. I will finally outline the on-going investigations (in collaboration with Salvatore G. Butera) in the direction of observing back-reaction effects of the quantum Hawking emission onto the black hole background.