Abstract: Relativistic theories of dissipative fluids have long been known to suffer from pathologies. In recent years, a novel consistent formulation has been proposed: a well-posed and causal version of the relativistic Navier-Stokes equations. This theory provides a promising alternative to existing approaches and represents a key development in the foundations of relativistic hydrodynamics. We will introduce this emergent framework, motivate its application in addressing state-of-the-art challenges, and present progress in numerical implementations. In particular, we will report on its success in describing experimental data from heavy-ion collisions at the LHC, providing a proof of principle that it offers a viable solution to the causality issues found in current models. We will also discuss ongoing work towards the simulations of viscous neutron star mergers.