Swinging between accretion and rotation power in binary millisecond pulsars

Neutron stars in low mass X-ray binaries are spun-up to millisecond spin periods during a Gyr-long phase of accretion of the matter transferred by a companion star. When the rate of mass transfer decreases at the end of this Gyr-long X-ray bright phase, a radio pulsar powered by the rotation of the neutron star magnetic field turns on. After decades of searches, the evolutionary link between these two classes of sources has been recently proven by the discovery of three sources that were observed to swing between accretion (X-ray bright) and rotation (radio bright) pulsar behaviour. These sources are the prototype of a new class of transitional systems that alternate between accretion and rotation-powered states in response to variations of the rate of mass in-flow, on time scales as short as a couple of weeks. Observations of this and other similar systems indicate that transitions to the accretion phase not only involve bright X-ray outbursts, but also a fainter intermediate X-ray state, possibly caused by centrifugal inhibition and ejection of the matter flow. Transitional ms pulsars are ideal test beds for theories describing the accretion-ejection coupling around a fast magnetized rotator, as well as the evolution of old binary systems. I will review the main observed properties, the prospects of catching more state transitions, and the possibilities to fully exploit the unique observable features of this newly established class.