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Metamaterials are composite structures whose extraordinary properties arise from a mesoscale organization of their constituents. Here, we introduce a different material class—viscosity metafluids. Specifically, we demonstrate that we can rapidly drive large viscosity oscillations in shear-thickened fluids using acoustic perturbations with kHz to MHz frequencies. Because the timescale for these oscillations can be orders of magnitude smaller than the timescales associated with the global material flow, we can construct metafluids whose resulting time-averaged viscosity is a composite of the thickened, high-viscosity and dethickened, low-viscosity states. We show that viscosity metafluids can be used to engineer a variety of unique properties including zero, infinite, and negative viscosities. The high degree of control over the resulting viscosity, the ease with which they can be accessed, and the variety of exotic properties achievable make viscosity metafluids attractive for uses in technologies ranging from coatings to cloaking to 3D printing. Published by the American Physical Society2024