Soft gamma repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are strange X-ray pulsars
showing slow rotations, bright soft X-rays, and recurrent burst activities. Based on accumulating
observational evidence, these pulsars are now thought to be magnetically powered neutron stars,
or “magnetars” with an extremely strong magnetic field of 1e+10-11 T. Such a field is by 2-3 orders
of magnitudes higher than those of normal neutron stars, and well above the quantum critical field,
4.4e+9 T, and sparking an interest not only in pulsar science but also in wide-ranging astrophysics,
even in particle physics or nuclear physics. Such a strong field is considered to induce characteristic
burst activities and particular X-ray spectra, little is known about how the magnetic energy is dissipated
and converted into the radiation. In order to provide an unified characterization of this class,
we performed a comprehensive study of broad-band X-ray spectra, and revealed the spectral
evolution correlated with their characteristic age and their magnetic field strength. I will also
introduce recent progress of X-ray observation of these mysterious X-ray sources and the future missions.