This minisymposium focuses on recent approaches in constitutive modelling of fluids with special emphasis on non-Newtonian flows which occur, for instance, in biological systems (blood) or lubricants (synthetic or natural). It is well-known that linear relations between the velocity gradient and the stress fail to accurately describe the material behaviour in such cases. Consequently, novel approaches are required for the constitutive modelling of fluids. A particular emphasis of this minisymposium is the advancement of scale-bridging material models for fluids as the vision is to overcome the burden of fine numerical discretizations which are still required today. To this end, temporal and/or spatial homogenization techniques might be a promising strategy as they have already proven beneficial for the modelling of solids. Possible topics for contributions of the minisymposium are: - Homogenization approaches - Modelling based on internal variables - Surrogate modelling - AI-based strategies - Adaptive parameter adjustment - Experimental investigations - Mathematical analysis