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This book explores one-dimensional nonequilibrium systems, both classical and quantum, using extensive numerical simulations and advanced field-theoretical methods, namely the functional renormalization group. It weaves unexpected connections between classical statistical physics with the Kardar-Parisi-Zhang (FRG) equation, which is a famous model for stochastic interface growth; dynamical systems, with the complex Ginzburg-Landau (CGL) equation, which is a much-studied model of deterministic chaos; exciton-polariton fluids-elementary opto-electronic excitations created in dedicated semiconductor nanostructures-which are subject to a non-equilibrium Bose-Einstein transition. This work unveils a new fixed point of the one-dimensional KPZ equation, named inviscid Burgers (IB) fixed point, which had been missed so far, and which yields a new scaling regime in the limit of small surface tension (or small viscosity in the equivalent Burgers equation). It turns out that the IB fixed point also emerges in the CGL equation, in particular in the regime known as phase turbulence, where the phase correlations at intermediate wavenumbers are shown to systematically exhibit the IB universal scaling properties. Besides, the phase diagram of exciton-polaritons is fully determined and highlights the existence of three phases beyond the KPZ one, a soliton-patterned regime at large interactions and weak noise; a vortex-disordered regime at high noise and weak interactions; and a defect-free reservoir-textured regime when the adiabatic approximation breaks down.