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 MacPherson’s norm maps on Chow groups as well as Voevodsky’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.