  Well before the radio discovery of pulsars offered the first observational
confirmation for their existence (Hewish et al., 1968), it had been suggested
that neutron stars might be endowed with very strong magnetic fields of
$10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their
magnetic fields that these otherwise small ed inert, cooling dead stars emit
radio pulses and shine in various part of the electromagnetic spectrum. But the
presence of a strong magnetic field has more subtle and sometimes dramatic
consequences: In the last decades of observations indeed, evidence mounted that
it is likely the magnetic field that makes of an isolated neutron star what it
is among the different observational manifestations in which they come. The
contribution of the magnetic field to the energy budget of the neutron star can
be comparable or even exceed the available kinetic energy. The most magnetised
neutron stars in particular, the magnetars, exhibit an amazing assortment of
explosive events, underlining the importance of their magnetic field in their
lives. In this chapter we review the recent observational and theoretical
achievements, which not only confirmed the importance of the magnetic field in
the evolution of neutron stars, but also provide a promising unification scheme
for the different observational manifestations in which they appear. We focus
on the role of their magnetic field as an energy source behind their persistent
emission, but also its critical role in explosive events.
