The Milnor conjectures relating the graded Witt ring and the mod-2 Galois cohomology ring of a field have been a driving force in the algebraic theory of quadratic forms. The degree 2 norm
residue isomorphism, due to Merkurjev, established the first case of the Milnor conjectures and ushered in a new era in the theory of quadratic forms. We shall explain some of the consequences of the
Milnor conjectures, with particular reference to invariants of fields associated to quadratic forms.