Recent Developments in Relativistic Hydrodynamic Fluctuations

The study of thermal fluctuations in relativistic hydrodynamics has led to numerous important developments in the last decade. We present a bird's eye view of the recent advances on the theory of fluctuations on three fronts; stochastic hydrodynamics, hydro-kinetics where fluctuations are included as additional modes that satisfy deterministic evolution equations, and effective field theory formulation of relativistic hydrodynamics. We compare and contrast these different but complimentary frameworks and highlight various recent progresses in each of them.