Oscillating grid systems are common tools used by experimentalists to generate well controlled and supposedly homogeneous and isotropic turbulence, and study its interaction with various other objects or phenomena (density stratification, sedimentation, bubbles, non-Newtonian fluid properties, interfacial gas-liquid mass transfer, and so on). However, such devices are not as easy to operate and as efficient in generating zero-mean shear turbulence as they are thought of, especially when confronted to rheological complexity. They thus remain to this day poorly exploited beyond fundamental research, despite an interesting potential for some industrial applications. This talk will introduce and study complexity in oscillating grid turbulence in two ways: firstly, by considering flow of non-Newtonian, shear-thinning fluids, and secondly by presenting first results of fractal oscillating grids oscillating in water. Results from experiments performed on various test sections with several optical methods (PIV, PTV, PLIF …) will be presented. In the first part, the effects of shear-thinning rheology on mean flow intensification, turbulence propagation and decay, and energy transfer mechanisms will be discussed. In the second part, the flow generated by fractal grids of various geometries oscillating in water will be analysed in a similar way in order to describe turbulence, oscillatory flows, and mean flow properties. Both paths will eventually converge, as the possibility of using novel fractal oscillating grid system as a way to enhance mixing in shear-sensitive complex biological fluids will be mentioned.