In the future, advanced reactors are expected to play an important role in nuclear power. However, their development and deployment are hindered by the absence of reliable and efficient models for analysis of system thermal hydraulics (TH). For instance, mixing and thermal stratification in reactor enclosures cannot be captured by traditional one-dimensional system codes, yet usage of high-resolution solvers is computationally expensive. Recent developments of coarse grid (CG) and system codes with three-dimensional capabilities have shown that they are promising tools for system-level analysis. However, these codes feature large turbulence model form and discretization errors and require further improvements to capture turbulent effects during complex transients. Improvements can be achieved by using data-driven (DD) approaches. This paper provides an overview of recent applications of DD methods in the areas of fluid dynamics and TH. It is demonstrated that they are being widely applied for engineering-scale analysis (e.g., closures for large eddy simulations/Reynolds-averaged Navier-Stokes using direct numerical simulation data). However, they cannot be directly employed for the system scale because of some features of the latter: usage of CG, transient nature of the considered phenomena, nonlinear interaction of multiple closures, etc. At the same time, accumulated experience allows outlining of potential frameworks for further developments in DD CG modeling of system-level TH.