We discuss several aspects of the coherent quantum dynamics of bio-molecular systems and more generally complex networks in the presence of an environment. Three general points will be addressed. Firstly, we identify fundamental structural elements underlying the quantum dynamics of these systems. Secondly, we provide novel approaches to the description of the quantum dynamics of complex networks when the coupling to the environment is neither perturbative nor so strong as to enforce fully classical dynamics. Thirdly, we discuss possible approaches towards deciding and quantify the non-classicality of the action of the environment and the observed system-dynamics on the basis of actual experimental data.