The parametric generation of quantum states of light holds a central position across various fields of quantum technologies. Starting from the seminal experiments in the 1970’s, we retrace the history of this powerful approach for creating and tailoring entangled photon pairs or squeezed states of light from the interaction of strong laser fields with optically nonlinear media. From its inception to its latest applications, this technique not only continues to play a pivotal role in the burgeoning fields of quantum computation, communication, and metrology, but shares also fundamental links with general concepts of quantum field theories in curved space-times.