Spiders are a new class of millisecond pulsars in binary systems: the so-called black widows feature a very low-mass stellar companion (typically Mc <0.05 Msol), and the so-called redbacks a low mass companion ( 0.1Msol < Mc < 0.5 Msol typically) which in both cases orbits very closely the pulsar with periods of a few hours only. What are the consequences of the promiscuity between the pulsar and the companion ? We will see that the companion is litteraly being evaporated by the pulsar, raising the question of its eventual disappearance. Pulsar timing also allows to measure strong irregularities of the orbital motion, which can only be explained by a coupling with the internal structure of the companion, and contribute to hinder the use of these pulsars in timing arrays for gravitational-wave detections. Conversely, these effects result in new observables covering almost every wavelength. These are as many new windows to measure the properties of the companion structure, the pulsar wind, the orbital dynamics, provided we can model the observations...