Light sources based on accelerators aim at producing very high brilliance coherent radiation, tuneable from the infrared to X-ray range, with picosecond or femtosecond light pulses.The first synchrotron light sources were built around storage rings in which a large number of relativistic electrons produce "synchrotron radiation" when their trajectory is subjected to a magnetic field, either in bending magnets or in specific insertion devices (undulators), made of an alternating series of magnets, allowing the number of curvatures to be increased and the radiation to be reinforced.These "synchrotron radiation" storage rings are now used worldwide (there are more than thirty), and they simultaneously distribute their radiation to several tens of users around the storage ring.The most effective installations in term of brilliance are the so-called 3rd generation synchrotron radiation light sources. The radiation produced presents pulse durations of the order of a few tens of ps, at a high rate (of the order of MHz); it is tuneable over a large range, depending on the magnetic field and the electron beam energy and its polarisation is adjustable (in the VUV-soft-X range). Generally, a very precise spectral selection is made by the users with a monochromator.The single pass linear accelerators can produce very short electron bunches (∼ 100 femtosecond). The beam of very high electronic density is sent into successive undulator modules, reinforcing the radiation's longitudinal coherence, produced according to a Free Electron Laser (FEL) scheme by the interaction between the electron bunch and a light wave. The very high peak brilliance justifies their designation as 4th generation sources. The number of users is smaller because an electron pulse produces a radiation burst towards only one beamline. Energy Recovery Linacs (ERL) let the beam pass several times in the accelerator structures either to recover the energy or to accelerate the electrons during several turns, and thus provide subpicosecond beams for a greater number of users.A state-of-the-art of X sources using conventional (and not laser plasma based) accelerators is given here, underlying the performance already reached or forecast and the essential challenges.