In a frustrated magnet, spins must decide between a large number of
degenerate ground states.  This impedes the development of magnetic
order and may lead to the formation of unusual thermodynamic phases
and quantum vacua, as well as to increased sensitivity to nominally
small perturbations.  A classic example is the Ising antiferromagnet
on the triangular lattice: its spins exhibit power-law correlations
at zero temperature.  I will review the experimental properties and
theoretical understanding of strongly frustrated magnets, with emphasis
on the pyrochlore family.