There is a growing body of evidence that two classes of cosmic high-energy sources, the Soft Gamma Repeaters, SGRs, and the Anomalous X-ray Pulsars, AXPs, contain slowly spinning ~5-10 s "magnetars'', i.e. neutron stars the emission of which is powered by the release of energy from their extremely strong magnetic fields (>10^15 G). I survey the main characteristics of these sources and the way they are interpreted within the magnetar scenario. The giant flare of Dec 27, 2004 from SGR 1806-20 has opened a new perspective in the study of magnetars' emission properties, from infrared wavelengths to gravitational waves, and structure.