  The reversal time (superparamagnetic relaxation time) of the magnetization of
fine single domain ferromagnetic nanoparticles owing to thermal fluctuations
plays a fundamental role in information storage, paleomagnetism, biotechnology,
etc. Here a comprehensive tutorial-style review of the achievements of fifty
years of development and generalizations of the seminal work of Brown [W.F.
Brown, Jr., Phys. Rev., 130, 1677 (1963)] on thermal fluctuations of magnetic
nanoparticles is presented. Analytical as well as numerical approaches to the
estimation of the damping and temperature dependence of the reversal time based
on Brown's Fokker-Planck equation for the evolution of the magnetic moment
orientations on the surface of the unit sphere are critically discussed while
the most promising directions for future research are emphasized.
