  The stability of the spin of pulsars and the precision with which these spins
can be determined, allows many unique tests of interest to physics and
astrophysics. Perhaps the most challenging and revolutionary of these, is the
detection of nanohertz gravitational waves. An increasing number of efforts to
detect and study long-period gravitational waves by timing an array of pulsars
have been ongoing for several decades and the field is moving ever closer to
actual gravitational-wave science. In this review article, we summarise the
state of this field by presenting the current sensitivity to gravitational
waves and by reviewing recent progress along the multiple lines of research
that are part of the continuous push towards greater sensitivity. We also
briefly review some of the most recent efforts at astrophysical interpretation
of the most recent GW estimates derived from pulsar timing.
