In this talk we discuss the partial regularity theory for suitable weak solutions to the equations describing incompressible power law fluids in the shear thickening case $p>2$. These systems constitute a nonlinear generalization of the classical Navier–Stokes equations, where the viscosity depends on the shear rate through a power law constitutive relation. After introducing the notion of suitable weak solutions based on a local energy inequality involving a local pressure projection, we present a new $\var $-regularity criterion formulated in terms of scaling invariant quantities associated with the gradient of the velocity field. The analysis is based on intrinsic scaling methods adapted to the nonlinear structure of the $p$-Stokes operator together with decay estimates for localized energy quantities. The main result establishes that smallness of a suitable scaling invariant norm implies local smoothness of the weak solution. As a consequence, we obtain an estimate on the size of the singular set in terms of parabolic Hausdorff measure. The proof combines compactness arguments, decay lemmas, localized pressure estimates, and embeddings. The talk emphasizes the similarities and differences between the regularity theory for the Navier–Stokes equations and for generalized Newtonian fluids with shear thickening viscosity.