Chemical energy carriers will play an essential role for future energy systems, where harvesting and utilization of renewable energy occur not necessarily at the same time or place, hence long-time storage and long-range transport of energy are needed. For this, hydrogen holds great promise. Its utilization by combustion-based energy conversion has many advantages, e.g., versatile use for heat and power, robust and flexible technologies, and its suitability for a continuous energy transition. However, combustion of hydrogen is very challenging. High temperatures lead to emissions of nitrogen oxides and high burning velocities and low flammability limits to potential flash-back and safety issues. Further, intrinsic, so-called thermo-diffusive instabilities occur, which can substantially increase burn rates by factor of up to 3-5 (!). Here, we will discuss relevant properties of hydrogen and provide examples for their importance. Further, results from studies on intrinsic instabilities in laminar and turbulent settings will be presented and analyzed.