Abstract: The theory of relativistic hydrodynamics has been very successful due to its wide range of applications. However, the theory is not complete as a deterministic theory as it ignored thermal fluctuations. Recent experiments in the Relativistic Heavy Ion Collider at BNL and the Large Hadron Collider at CERN show that the quark-gluon plasma created in these experiments can be well described with relativistic hydrodynamics. The size of the system is also small enough for fluctuations to be observable. Additionally, studying hydrodynamic fluctuations provides a way to search for the QCD critical point because the fluctuations become more pronounced near the critical point, so does the non-Gaussianity of the fluctuations. In this talk, I will introduce the theoretical background and recent progress of the theory of hydrodynamic fluctuations. I will also discuss our contributions and present our calculations of the non-Gaussian fluctuations in the Bjorken flow, as well as the finding that a field re-definition is needed to study non-Gaussian fluctuations in hydrodynamics.