Insights into the astrophysics of supermassive black hole binaries from pulsar timing observations

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.