The celebrated Milnor conjecture establishes a deep connection between Milnor \$K\$-theory and Galois cohomology of a field \$k\$, which in this case can be identified with étale cohomology. Its proof by Voevodsky, via the introduction of motivic cohomology, marked a foundational development in motivic homotopy theory. As a consequence, it also provides a key step toward the Lichtenbaum--Quillen conjecture. In this talk, I will begin by introducing étale cohomology and then present Voevodsky’s norm residue theorem. I will briefly explain its relationship to the Lichtenbaum--Quillen conjecture. As an application, I will discuss the computation of the motivic cohomology of a point over real closed fields and present a small recent result of my own in this direction.