Abstract: Historically, precision spectroscopy led to the discovery of quantum mechanics, to the confirmation of quantum electrodynamics, and lately to several Nobel Prizes in high-precision laser physics. In modern astrophysics, remarkable improvements in precision and stability of high-resolution spectrographs give them a unique role in the search for new physics. I provide two specific examples that illustrate this point. The first are tests of the universality of physical laws, through tests of the stability of nature's fundamental couplings. I will present recent ESPRESSO measurements and discuss some of their implications for relevant cosmological paradigms. The second is the exciting prospect of seeing the universe expand in real time, a.k.a. the redshift drift. The first dedicated such experiment has recently started at ESPRESSO. This is a proof-of-concept of, and possibly also a first epoch for, its expected detection by the ANDES spectrograph at the ELT.