Accreting Pulsars: Mixing-up Accretion Phases in Transitional Systems

In the last 20 years our understanding of the millisecond pulsar (MSP)population changed dramatically. Thanks to RXTE, we discovered that neutronstars in LMXBs spins at 200-750 Hz frequencies, and indirectly confirmed therecycling scenario, according to which neutron stars are spun up to ms periodsduring the LMXB-phase. In the meantime, the continuous discovery ofrotation-powered MSPs in binary systems in the radio and gamma-ray band (mainlywith the Fermi LAT) allowed us to classify these sources into two "spiders"populations, depending on the mass of their companion stars: Black Widow, withvery low-mass companion stars, and Redbacks, with larger companions possiblyfilling their Roche lobes but without accretion. It was soon regained that MSPsin short orbital period LMXBs are the progenitors of the spider populations ofrotation-powered MSPs, although a direct link between accretion- androtation-powered MSPs was still missing. In 2013 XMM-Newton spotted the X-rayoutburst of a new accreting MSP (IGR J18245-2452) in a source that waspreviously classified as a radio MSP. Follow up observations of the source whenit went back to X-ray quiescence showed that it was able to swing betweenaccretion- to rotation-powered pulsations in a relatively short timescale (fewdays), promoting this source as the direct link between the LMXB and the radioMSP phases. Following discoveries showed that there exists a bunch of sources,which alternates X-ray activity phases, showing X-ray pulsations, to radio-loudphases, showing radio pulsations, establishing a new class of MSPs: theTransitional MSP. In this review we describe these exciting discoveries and theproperties of accreting and transitional MSPs, highlighting what we know andwhat we have still to learn about in order to fully understand the (sometimepuzzling) behavior of these systems and their evolutive connection (abridged).