High-speed turbulent flows of real gases are encountered in many industry-related applications, ranging from energy production to wind tunnel testing and space exploration. With the term "real gas", we refer to the non-ideal thermodynamic behaviour caused either by the molecular complexity of the working fluid or by thermochemical non-equilibrium flow operating conditions, having both a significant influence on turbulence at high Mach numbers. Carrying out high-fidelity numerical simulations of such flows requires numerical schemes robust enough to handle strong discontinuities while ensuring low amounts of intrinsic dissipation in smooth flow regions. In this talk, we will discuss the influence of real-gas effects on compressible turbulence dynamics. After presenting a high-order shock-capturing scheme based on Jameson's artificial diffusivity methodology, we will first focus on turbulent flows of dense gases. For thermodynamic conditions close to the saturation curve, these heavy fluids may exhibit non-classical phenomena such as opposite speed of sound evolution along isentropic perturbations or even rarefaction shockwaves. Despite the large compressibility, they bear many similarities with incompressible flows, and most of their peculiar features in wall-bounded flows can be related to a liquid-like behaviour of the transport properties. In the second part of the talk, we will address the effects of high-enthalpy conditions typical of planetary atmosphere reentry bodies or hypersonic aircraft. Specifically, finite-rate chemistry and thermal relaxation phenomena will be evaluated in a flat-plate boundary layer configuration, encompassing the laminar, transitional and fully-turbulent regimes.