From concentrated solar power plants to rocket engines, energy conversion systems are continually reengineered to perform ever better. Often this involves fluids being pushed into the supercritical region, where highly non-ideal thermodynamic effects are at play. Yet, our fundamental understanding of flow physics at such conditions lags behind to successfully realize these exciting engineering applications. Especially, the sharp variations in all thermophysical properties close to the critical point and the high optical density at supercritical pressures lead to significantly richer flow physics and even more intricate phenomena in turbulence. In this talk we will present our recent fundamental on turbulence in supercritical fluids, which are relevant in all component of a supercritical power cycle. We will elucidate how and when flows with supercritical fluids transition to turbulence and how compressible effects can be characterized and modelled for turbulent heat transfer.