Neutron stars are enigmatic compact objects characterized by dense nuclear matter, rapid stellar rotation, and strong magnetic fields. Such an extreme environment has provided an accessible astrophysical laboratory to test fundamental physics. Recent astronomical observations from radio to gamma-rays have revealed a remarkable diversity of neutron stars: e.g., rotation-powered pulsars, accretion-powered pulsars, and magnetically-powered sources. Among important physical parameters of neutron stars, a wide range of magnetic field from 1e+4 T to 1e+11 T is thought to be one principal cause of the diversity. Especially, enigmatic X-ray sources, Soft Gamma Repeater (SGRs) and Anomalous X-ray Pulsar (AXPs), are now considered to have extremely strong magnetic field reaching 1e+10--1e+11 T, and thus, dubbed as "magnetars". They emerge mainly in the X-ray frequency with intense giant flares, short bursts, and X-ray outbursts. Unlike for rotation-powered or accretion-powered pulsars, the bulk of their X-ray emission appears to be powered by their super-strong magnetic fields. At this talk, I will review recent high energy astrophysical observations of strongly-magnetized neutron stars, and also overview approved future missions to approach the neutron star science.