The theory of double beta decay is briefly reviewed. The most recent (2015) results for 0νβ −β − nuclear matrix elements in the interacting boson model (IBM-2) with light and heavy neutrino exchange are given for all nuclei of interest from 48Ca to 238U. The question of quenching of the axial vector coupling constant gA in nuclei is discussed. Possible additional scenarios, such as Majoron emission, and mechanisms, such as sterile neutrino exchanges, are also discussed.