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Normed motivic spectra are motivic spectra equipped with a coherent system of multiplicative norms along finite etale maps. Many motivic spectra of interest admit canonical normed structures, e.g. the motivic cohomology spectrum, the algebraic K-theory spectrum, and the algebraic cobordism spectrum. For example, the normed structure on HZ underlies Fulton and MacPhersonâ s norm maps on Chow groups as well as Voevodskyâ s power operations in motivic cohomology. Among other things, the formalism of normed spectra allows us to extend the Fulton-MacPherson norms to Chow groups in mixed characteristic and to Chow-Witt groups. This is joint work with Tom Bachmann.