  We outline the eccentricity evolution of sub-parsec massive black hole
binaries (MBHBs) forming in galaxy mergers. In both stellar and gaseous
environments, MBHBs are expected to grow large orbital eccentricities before
they enter the gravitational wave (GW) observational domain. We re--visit the
predicted eccentricities detectable by space based laser interferometers (as
the proposed ELISA/NGO) for both environments. Close to coalescence, many MBHBs
will still maintain detectable eccentricities, spanning a broad range from
<10^{-5} up to <~ 0.5. Stellar and gas driven dynamics lead to distinct
distributions, with the latter favoring larger eccentricities. At larger binary
separations, 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 proposed
electromagnetic counterparts to the GW signal, which we briefly review.
