Though they are also referred to as ‘soft matter’, we designate by ‘complex fluids’ fluids whose microstructure contains specific components (the solute) having sizes and relaxation timescales much larger than those of the atoms/molecules of the ‘simple fluid’ (the solvent) in which they are embedded. The differences between the dynamical behavior of simple and complex fluids is worth describing. In simple fluids, the microstructure remains regular and locally well-described by classical equilibrium statistical mechanics regardless of whether the material is flowing or is at rest. At the hydrodynamical level of description, this is reflected by the linear force-flux relations, such as the Newton, Fick and Fourier laws. In complex fluids, e.g. polymeric fluids, colloidal suspensions, liquid crystals, etc., the slow and non-equilibrium response of the solute usually implies more involved rheological laws. To avoid formulating these rheological properties at the macroscopic level of description, one approach consists in adding structural variables to the state vector and proposing a coarse-grained model to capture the solute response to external forces. Given the correspondences with the PDF approach, it is interesting to investigate the connections between complex fluids and turbulent dispersed two-phase flows.