Informally speaking, the essential dimension of an algebraic object is the minimal number of independent parameters needed to define it. We will explain how valuations can be used to prove lower bounds on the essential dimension of Galois cohomology classes of a field (with an emphasis on the Brauer group). If time permits, analogous results for Witt classes of Hermitian forms generalizing a theorem of Chernousov and Serre will be discussed. This is joint work with Zinovy Reichstein.