  Casimir and Casimir-Polder repulsion have been known for more than 50 years.
The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs
permits repulsion if they are separated by a dielectric fluid that has a value
of permittivity that is intermediate between those of the dielectric slabs.
This was indirectly confirmed in the 1970s, and more directly by Capasso's
group recently. It has also been known for many years that electrically and
magnetically polarizable bodies can experience a repulsive quantum vacuum
force. More amenable to practical application are situations where repulsion
could be achieved between ordinary conducting and dielectric bodies in vacuum.
The status of the field of Casimir repulsion with emphasis on recent
developments will be surveyed. Here, stress will be placed on analytic
developments, especially of Casimir-Polder (CP) interactions between
anisotropically polarizable atoms, and CP interactions between anisotropic
atoms and bodies that also exhibit anisotropy, either because of anisotropic
constituents, or because of geometry. Repulsion occurs for wedge-shaped and
cylindrical conductors, provided the geometry is sufficiently asymmetric, that
is, either the wedge is sufficiently sharp or the atom is sufficiently far from
the cylinder.
