Turbulent reacting flows are pervasive both in our daily lives on Earth and in the Universe. They power modern energy generation and propulsion systems, such as gas turbines, internal combustion and jet engines. At the same time, they also have tremendous destructive potential being the primary driver of the majority of gaseous explosions. On astronomical scales, thermonuclear turbulent flames are at the core of some of the most powerful explosions in the Universe, known as Type Ia supernovae. These are crucibles, in which most of the elements around us from oxygen to iron are synthesized, and in the last 15 years they have been used as cosmological distance probes to discover the existence of dark energy. Despite this ubiquity in Nature, turbulent reacting flows remain poorly understood still posing a number of fundamental questions. In this talk I will give an overview of the numerical and theoretical work at the Naval Research Laboratory over the recent years aimed at studying both chemical and thermonuclear turbulent flames. I will highlight several surprising phenomena that have emerged in the course of this work, in particular, in the context of the intrinsic instabilities of high-speed turbulent flames. Finally, I will briefly discuss the implications of this work for the development of accurate, predictive turbulent flame models required for the design of practical combustion applications.