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Over the last decade the gradient-flow formalism became a widely used tool for lattice simulations of QCD. In my talk I will introduce the formalism and focus on aspects for which perturbative input can help to extract physical observables from lattice calculations. A particularly powerful tool is the flowed operator product expansion to express operators through their better behaved flowed counterparts which do not require renormalization. I will show how it can be used to define the energy-momentum tensor of QCD on the lattice and how it can be applied to the effective electroweak Hamiltonian of flavor physics.