  Pulsar timing arrays (PTAs) are designed to detect the predicted
gravitational wave (GW) background produced by a cosmological population of
supermassive black hole (SMBH) binaries. In this contribution I review the
physics of such GW background, highlighting its dependence on the overall
binary population, the relation between SMBHs and their hosts, and their
coupling with the stellar and gaseous environment. The latter is particularly
relevant when it drives the binaries to extreme eccentricities (e>0.9), which
might be the case for stellar-driven systems. This causes a substantial
suppression of the low frequency signal, potentially posing a serious threat to
the effectiveness of PTA observations. A future PTA detection will allow to
directly observe for the first time subparsec SMBH binaries on their way to the
GW driven coalescence, providing important answers of the outstanding questions
related to the physics underlying the formation and evolution of these
spectacular sources.
