  Magnetars are the strongest magnets in the present universe and the
combination of extreme magnetic field, gravity and density makes them unique
laboratories to probe current physical theories (from quantum electrodynamics
to general relativity) in the strong field limit. Magnetars are observed as
peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and
the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares,"
extremely powerful events during which luminosities can reach up to 10^47 erg/s
for about one second. The last five years have witnessed an explosion in
magnetar research which has led, among other things, to the discovery of
transient, or "outbursting," and "low-field" magnetars. Substantial progress
has been made also on the theoretical side. Quite detailed models for
explaining the magnetars' persistent X-ray emission, the properties of the
bursts, the flux evolution in transient sources have been developed and
confronted with observations. New insight on neutron star asteroseismology has
been gained through improved models of magnetar oscillations. The long-debated
issue of magnetic field decay in neutron stars has been addressed, and its
importance recognized in relation to the evolution of magnetars and to the
links among magnetars and other families of isolated neutron stars. The aim of
this paper is to present a comprehensive overview in which the observational
results are discussed in the light of the most up-to-date theoretical models
and their implications. This addresses not only the particular case of magnetar
sources, but the more fundamental issue of how physics in strong magnetic
fields can be constrained by the observations of these unique sources.
