  The discovery in 2000 that the ferromagnetic (FM) compound UGe2 (T_Curie = 52
K at ambient pressure) becomes superconducting under a pressure of P = 1.1 GPa
until it enters the paramagnetic (PM) phase above Pc = 1.6 GPa was a surprise.
Successive searches for new materials (URhGe and UCoGe) led to the discovery of
the coexistence of superconductivity (SC) and ferromagnetism at ambient
pressure. Furthermore in UCoGe, it was found that SC survives in the PM regime
from P_c = 1.1 to 4 GPa. Focus has been on low-temperature experiments under
extreme conditions of magnetic field (H), pressure, and uniaxial stress. In
UGe2, strong interplay exists between Fermi surface (FS) reconstructions in the
cascade of different FM and PM ground states and their magnetic fluctuations.
Similar phenomena occur in URhGe and UCoGe but, at first glance, the SC seems
to be driven by the FM fluctuations. In UCoGe, a longitudinal field scan leads
to a drastic decrease in the FM fluctuations, while a transverse field scan
leads to suppression of the Curie temperature, T_Curie; the consequence is a
boost in FM fluctuations, leading to a reinforcement of SC. The singularity in
URhGe is the weakness of the anisotropy between c- and b-axes; the most
noteworthy feature is the detection of reentrant SC near H_R. All the
experimental results give evidence that the SC in these three materials
originates from the FM fluctuations, which are amplitude modes of magnetic
excitations in the FM state. Spin-triplet pairing has been anticipated in the
FM superconductors and was actually observed by Knight-shift measurements in
the SC state of UCoGe. Their fascinating (p, T, H) phase diagrams are now well
established. Discussion is presented on how different theoretical approaches
can describe the various phenomena discovered by experimentalists.
