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In this paper, we construct a refined, relative version of the \'etalerealization functor of motivic spaces, first studied by Isaksen and Schmidt.Their functor goes from the $\infty$-category of motivic spaces over a basescheme $S$ to the $\infty$-category of $p$-profinite spaces, where $p$ is aprime which is invertible in all residue fields of $S$.  In the first part of this paper, we refine the target of this functor to an$\infty$-category where $p$-profinite spaces is a further completion. Roughlyspeaking, this $\infty$-category is generated under cofiltered limits by thosespaces whose associated "local system" on $S$ is $A^1$-invariant. We thenconstruct a new, relative version of their \'etale realization functor whichtakes into account the geometry and arithmetic of the base scheme $S$. Forexample, when $S$ is the spectrum of a field $k$, our functor lands in acertain $\infty$-category equivariant for the absolute Galois group. Ourconstruction relies on a relative version of \'etale homotopy types in thesense of Artin-Mazur-Friedlander, which we also develop in some detail,expanding on previous work of Barnea-Harpaz-Schlank.  We then stabilize our functor, in the $S^1$-direction, to produce an \'etalerealization functor for motivic $S^1$-spectra (in other words, Nisnevichsheaves of spectra which are $A^1$-invariant). To this end, we also develop an$\infty$-categorical version of the theory of profinite spectra, first exploredby Quick. As an application, we refine the construction of the \'etale$K$-theory of Dwyer and Friedlander, and define its non-commutative extension.This latter invariant should be seen as an $\ell$-adic analog of Blanc's theoryof semi-topological $K$-theory of non-commutative schemes. We then formulateand prove an analog of Blanc's conjecture on the torsion part of this theory,generalizing the work of Antieau and Heller.

Relative \'{E}tale Realizations of Motivic Spaces and Dwyer-Friedlander $K$-Theory of Noncommutative Schemes