There exist a fair number of insulating magnetic materials where the
magnetic species is a 4f (rare-earth) element and which have been
long known to display interesting and intriguing magnetic and
thermodynamic behaviors. Examples include the three-dimensional
Gd3Ga5O12 garnet (GGG) lattice of corner-sharing tetrahedra,
the LiHo_xY_{1-x}F4 Ising material in a transverse magnetic field (TFIM),
and a number of pyrochlore systems such as the Tb2Ti2O7 spin liquid,
the spin Dy2Ti2O7 and Ho2Ti2O7 spin ices and the Gd2(Ti,Sn)2O7 long-range
ordered systems. In this talk, I will review some of the problems motivated
by experiments on these systems, discuss tentative explanations of what is
maybe going on and emphasize what we do not understand.
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