Abstract: Since Amitsur settled the long standing fundamental open problem of existence of noncrossed products, their existence over familiar fields was an object of investigation. In the first talk, we describe a fundamental valuation theoretic argument (original to Eric Brussel) which led to the discovery of noncrossed products over Henselian valued fields F with global residue field. In the second talk, we shall describe the "location" of noncrossed products in the Brauer group of F by proving the existence of certain bounds on the index that, roughly speaking, separate crossed and noncrossed products. (Joint with Jack Sonn.)