Embedded contact homology, due to Michael Hutchings, is an invariant of 3-manifolds (with a distinguished second homology class, corresponding to the choice of a spin"c" structure in Seiberg–Witten Floer homology) isomorphic (by work of Clifford Taubes) to Seiberg–Witten Floer cohomology and consequently (by work announced by and ) to the plus-version of Heegaard Floer homology (with reverse orientation). It may be seen as an extension of Taubes's Gromov invariant, known to be equivalent to the Seiberg–Witten invariant, from closed symplectic 4-manifolds to certain non-compact symplectic 4-manifolds (namely, a contact three-manifold cross R). Its construction is analogous to symplectic field theory, in that it is generated by certain collections of closed Reeb orbits and its differential counts certain holomorphic curves with ends at certain collections of Reeb orbits. It differs from SFT in technical conditions on the collections of Reeb orbits that generate it—and in not counting all holomorphic curves with Fredholm index 1 with given ends, but only those that also satisfy a topological condition given by the "ECH index", which in particular implies that the curves considered are (mainly) embedded.