  We describe the Hodge theory of brilliant families of K3 surfaces. Their
characteristic feature is a close link between the Hodge structures of any two
fibres over points in the Noether-Lefschetz locus. Twistor deformations, the
analytic Tate-Safarevic group, and one-dimensional Shimura special cycles are
covered by the theory. In this setting, the Brauer group is viewed as the
Noether-Lefschetz locus of the Brauer family or as the specialization of the
Noether-Lefschetz loci in a family of approaching twistor spaces. Passing from
one algebraic twistor fibre to another, which by construction is a
transcendental operation, is here viewed as first deforming along the more
algebraic Brauer family and then along a family of algebraic K3 surfaces.
