  A non-technical introduction to the theory of magnets with strong geometric
frustration is given, concentrating on magnets on corner-sharing (kagome,
pyrochlore, SCGO and GGG) lattices. Their rich behaviour is traced back to a
large ground-state degeneracy in model systems, which renders them highly
unstable towards perturbations. A systematic classification according to
properties of their ground states is discussed. Other topics addressed in this
overview article include a general theoretical framework for thermal order by
disorder; the dynamics of how the vast regions of phase space accessible at low
temperature are explored; the origin of the featureless magnetic susceptibility
fingerprint of geometric frustration; the role of perturbations; and spin ice.
The rich field of quantum frustrated magnets is also touched on.
