This article is a survey on the authors' proof of the isomorphism between Heegaard Floer homology and embedded contact homology appeared in This article is a survey on the authors' proof of the isomorphism between Heegaard Floer homology and embedded contact homology appeared in arXiv:1208.1074, arXiv:1208.1077 and arXiv:1208.1526.
Comment: 69 pages, 10 figures. To appear in Characters in low-dimensional topology, Centre de Recherches Math\'ematiques Proceedings, Contemporary Mathematics. Version 2: several typos corrected