As a carbon-free carrier for renewable energies, hydrogen has the potential to contribute to the success of the energy transition. In addition to electrochemical applications, thermochemical applications will continue to play an important role in high-performance energy conversion such as advanced low-emission combustion systems. However, the combustion of hydrogen poses challenges due to its special thermophysical and reaction kinetic properties. Lean combustion is required to minimize primary nitrogen oxide (NO_x) formation. This can lead to thermodiffusive instabilities that affect the internal structures of the reaction zone, the fuel consumption rate, the local equivalence ratios, and the local gas temperatures, thereby affecting primary NO_x formation. The thermodiffusive instabilities have long been known and have been extensively described, primarily through theoretical studies and numerical simulations for simple combustion systems. However, their interaction with turbulence in practical combustion environments remains relatively unexplored, particularly in the context of complex, real-world technical applications. There are few experimental data quantifying the influence of thermodiffusive instabilities on the internal flame structure with respect to the turbulence level. Therefore, the aim of this review is to summarize recent experiments to quantitatively describe the interaction between thermodiffusive instabilities and turbulence. Combustion systems of increasing complexity are considered using laser-optical measurement techniques for elucidating local flame properties. While Raman/Rayleigh spectroscopy is used to quantitatively resolve internal flame structures for unconfined combustion systems, this is not easily possible for enclosed systems under pressure. Instead, the extent to which the reaction zone is affected by thermodiffusive instabilities in interaction with the turbulent flow field is quantitatively assessed using information from laser-induced fluorescence measurements. Consistent with all configurations presented here, the ratio of diffusive to convective time scales plays a critical role in the significance of thermodiffusive instabilities.