  In the last 25 years, a new generation of X-ray satellites imparted a
significant leap forward in our knowledge of X-ray pulsars. The discovery of
accreting and transitional millisecond pulsars proved that disk accretion can
spin up a neutron star to a very high rotation speed. The detection of MeV-GeV
pulsed emission from a few hundreds of rotation-powered pulsars probed particle
acceleration in the outer magnetosphere, or even beyond. Also, a population of
two dozens of magnetars has emerged. INTEGRAL played a central role to achieve
these results by providing instruments with high temporal resolution up to the
hard X-ray/soft gamma-ray band and a large field of view imager with good
angular resolution to spot hard X-ray transients. In this article, we review
the main contributions by INTEGRAL to our understanding of the pulsating hard
X-ray sky, such as the discovery and characterization of several accreting and
transitional millisecond pulsars, the generation of the first catalog of hard
X-ray/soft gamma-ray rotation-powered pulsars, the detection of polarization in
the hard X-ray emission from the Crab pulsar, and the discovery of persistent
hard X-ray emission from several magnetars.
