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We outline the eccentricity evolution of sub-parsec massive black holebinaries (MBHBs) forming in galaxy mergers. In both stellar and gaseousenvironments, MBHBs are expected to grow large orbital eccentricities beforethey enter the gravitational wave (GW) observational domain. We re--visit thepredicted eccentricities detectable by space based laser interferometers (asthe proposed ELISA/NGO) for both environments. Close to coalescence, many MBHBswill still maintain detectable eccentricities, spanning a broad range from<10^{-5} up to <~ 0.5. Stellar and gas driven dynamics lead to distinctdistributions, with the latter favoring larger eccentricities. At larger binaryseparations, when emitted GWs will be observed by pulsar timing arrays (PTAs),the expected eccentricities are usually quite large, in the range 0.01-0.7,which poses an important issue for signal modelling and detection algorithms.In this window, large eccentricities also have implications on proposedelectromagnetic counterparts to the GW signal, which we briefly review.

Origin and Implications of high eccentricities in massive black hole binaries at sub-pc scales