  Pulsar timing arrays (PTAs) are designed to detect gravitational waves (GWs)
at nHz frequencies. The expected dominant signal is given by the superposition
of all waves emitted by the cosmological population of supermassive black hole
(SMBH) binaries. Such superposition creates an incoherent stochastic
background, on top of which particularly bright or nearby sources might be
individually resolved. In this contribution I describe the properties of the
expected GW signal, highlighting its dependence on the overall binary
population, the relation between SMBHs and their hosts, and their coupling with
the stellar and gaseous environment. I describe the status of current PTA
efforts, and prospect of future detection and SMBH binary astrophysics.
