Turbulence in ``living’’ or active systems is a topical subject that has profound applications in biophysical systems such as dense bacterial suspensions, micro-tubule networks, or even artificial swimmers, to mention a few. One of the major theoretical efforts in this area has been on developing phenomenological models that can describe flows in these systems. In our research group, we are interested in using these phenomenological models to predict statistical properties such as transport coefficients under steady state. Recently, we proposed powerful scaling laws to predict diffusion coefficient in these liquids maintained in a fully developed turbulent state. Our theoretical predictions were strongly supported by direct numerical simulations of the turbulent flows. In this talk I will describe some of the salient features of our research endeavors pertinent to this subject. I will also provide a glimpse of the ongoing work that is aimed at developing an effective thermodynamics description for interacting particles that are embedded in this active turbulent flow.