  State surfaces are spanning surfaces of links that are obtained from link
diagrams guided by the combinatorics underlying Kauffman's construction of the
Jones polynomial via state models. Geometric properties of such surfaces are
often dictated by simple link diagrammatic criteria, and the surfaces
themselves carry important information about geometric structures of link
complements. State surfaces also provide a tool for studying relations between
Jones polynomials and topological invariants, such as the crosscap number or
invariants coming from geometric structures on link complements (e.g.
hyperbolic volume). This article is brief survey on some of the recent
applications of state surfaces.
