  Neutron stars are among the most fascinating astrophysical sources, being
characterized by strong gravity, densities about the nuclear one or even above,
and huge magnetic fields. Their observational signatures can be extremely
diverse across the electromagnetic spectrum, ranging from the periodic and
low-frequency signals of radio pulsars, up to the abrupt high-energy gamma-ray
flares of magnetars, where energies of ~10^46 erg are released in a few
seconds. Fast-rotating and highly magnetized neutron stars are expected to
launch powerful relativistic winds, whose interaction with the supernova
remnants gives rise to the non-thermal emission of pulsar wind nebulae, which
are known cosmic accelerators of electrons and positrons up to PeV energies. In
the extreme cases of proto-magnetars (magnetic fields of ~10^15 G and
millisecond periods), a similar mechanism is likely to provide a viable engine
for the still mysterious gamma-ray bursts. The key ingredient in all these
spectacular manifestations of neutron stars is the presence of strong magnetic
fields in their constituent plasma. Here we will present recent updates of a
couple of state-of-the-art numerical investigations by the high-energy
astrophysics group in Arcetri: a comprehensive modeling of the steady-state
axisymmetric structure of rotating magnetized neutron stars in general
relativity, and dynamical 3-D MHD simulations of relativistic pulsar winds and
their associated nebulae.
