It is now widely accepted that soft gamma repeaters and anomalous X-ray pulsars are the observational manifestations of magnetars, i.e. sources powered by their own magnetic energy. This view was supported by the fact that these "magnetar candidates" exhibited, without exception, a surface dipole magnetic field (as inferred from the spin-down rate) in excess of the electron critical field (≃ 4.4×10¹³ G). The recent discovery of fully qualified magnetars, SGR 0418+5729 and Swift J1822.3-1606, with dipole magnetic field well in the range of ordinary radio pulsars posed a challenge to the standard picture, showing that a very strong field is not necessary for the onset of magnetar activity (chiefly bursts and outbursts). Here we summarize the observational status of the low-magnetic-field magnetars and discuss their properties in the context of the mainstream magnetar model and its main alternatives.