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Gradient flow is a continuous smearing operation that can be interpreted as a real-space renormalization group transformation on coarse-grained expectation values. As such, gradient flow can be used to predict the non-perturbative renormalization group beta-function of a gauge-fermion system using techniques from lattice quantum field theory. In this seminar, I will show how gradient flow beta-functions can be used to determine both infrared fixed points in systems of interest to beyond Standard Model physics and the strong coupling constant of quantum chromodynamics. I will end by considering the use of similar gradient-flow-based methods for calculating running operator anomalous dimensions on the lattice.