Neutron stars are formed in supernova explosions. They manifest themselves in many different ways, for example, as pulsars, anomalous X-ray pulsars (AXPs) and soft γ-ray repeaters (SGRs) and the so-called ‘radio-quiet neutron stars’. These objects are made visible by high-energy processes occurring on their surface or in the surrounding region. In most of these objects, ultra-strong magnetic fields are a crucial element in the radio, optical, X-ray and gamma-ray emission processes which dominate the observed spectrum.