Heavy-ion collision experiments have provided overwhelming evidence that quarks and gluons can flow as a nearly frictionless, strongly interacting relativistic fluid 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 present the new developments that have contributed to redefine the onset of relativistic fluid dynamics and its extension towards the far-from-equilibrium regime. I will show how first-order theories that are causal and stable can be systematically derived from relativistic kinetic theory using a modification of the Chapman-Enskog series. The question of whether the relativistic hydrodynamic derivative expansion converges, or not, will also be discussed.