We describe detailed high-resolution numerical simulations of a class of shock-induced reactive turbulent mixing layers, where the scalar mixing, flow dynamics and combustion properties are driven by the Richtmyer-Meshkov (RM) instability. The 3D high-resolution, numerical simulations of a reacting RM turbulent mixing layer were performed with the astrophysical FLASH code, with modifications to describe chemical reactions and heat release relevant to combustion applications. In the numerical simulations, a Mach 1.58 shock traverses a diffuse, corrugated material interface separating Hydrogen at 1000 K and Oxygen at 300 K, so that local misalignments between pressure and density gradients induce baroclinic vorticity at the contact line. We study the evolution of the interface and the flame as the resulting RM instability grows through linear, nonlinear and turbulent stages. We develop a detailed understanding of the effects of heat release and combustion on the underlying flow properties by comparing our results with a baseline non-reacting RM flow. The shock-driven instability growth enhances mixing at the interface, thus creating the conditions for efficient burning at the flame site. Conversely, the presence of the flame has a profound effect on the instability growth rates through the action of associated combustion waves and heat release at the site of burning. We document the properties of the instability (growth rates, molecular mixing fraction) and the flame (fluctuations of mixture fraction, temperature, scalar dissipation rate) as well as the nature of the coupling between the two. We find the incident shock energizes the flow, increases the scalar dissipation rate, while decreasing the Damkohler number. In contrast, the subsequent nonlinear decay of the instability is accompanied by an increase in the Damkohler number. We provide simple models that link the scalar dissipation rate and other flame-critical quantities to easily measured RM instability properties such as the integral mix width and the molecular mixing parameter. Our findings are relevant to supernovae detonation, knocking in IC engines and scramjet performance, while the underlying flow problem defined here represents a novel canonical framework to understand the broader class of non-premixed turbulent flames.