Heavy-ion collision experiments have provided evidence that quarks and gluons, the elementary particles within protons and neutrons, can flow as a nearly frictionless, strongly interacting relativistic liquid over distance scales not much larger than the size of a proton. On the other hand, with the dawn of the multi-messenger astronomy era marked by the detection of a binary neutron star merger, it became imperative to understand how extremely dense fluids behave under very strong gravitational fields. Therefore, cutting-edge experimental apparatus in modern science, such as the Relativistic Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC), and the Laser Interferometer Gravitational-Wave Observatory (LIGO), are now taking data whose description requires pushing the boundaries of our current understanding of fluid dynamics. In this talk, I will discuss the new developments that have contributed to redefining the onset of relativistic fluid dynamics and its extension towards the far-from-equilibrium regime. New results will also be presented involving viscous fluids and their coupling to general relativity. These developments pave the way for including viscous effects in state-of-the-art neutron star merger simulations.