  Superconductivity has again become a challenge following the discovery of
unconventional superconductivity. Resistance-free currents have been observed
in heavy-fermion materials, organic conductors and copper oxides. The discovery
of superconductivity in a single crystal of $UGe_2$, $ZrZn_2$ and $URhGe$
revived the interest in the coexistence of superconductivity and
ferromagnetism. The experiments indicate that: i)The superconductivity is
confined to the ferromagnetic phase. ii)The ferromagnetic order is stable
within the superconducting phase (neutron scattering experiments). iii) The
specific heat anomaly associated with the superconductivity in these materials
appears to be absent. The specific heat depends on the temperature linearly at
low temperature.
  I present a review of the recent experimental results and the basic
theoretical ideas concerning ferromagnetic superconductivity
(FM-superconductivity) induced by the ferromagnetic spin fluctuations. A
particular attention is paid to the magnon exchange mechanism of
FM-superconductivity.
