  We review recent theoretical and experimental advances toward understanding
the effects of nuclear spins in confined nanostructures. These systems, which
include quantum dots, defect centers, and molecular magnets, are particularly
interesting for their importance in quantum information processing devices,
which aim to coherently manipulate single electron spins with high precision.
On one hand, interactions between confined electron spins and a nuclear-spin
environment provide a decoherence source for the electron, and on the other, a
strong effective magnetic field that can be used to execute local coherent
rotations. A great deal of effort has been directed toward understanding the
details of the relevant decoherence processes and to find new methods to
manipulate the coupled electron-nuclear system.
  A sequence of spectacular new results have provided understanding of
spin-bath decoherence, nuclear spin diffusion, and preparation of the nuclear
state through dynamic polarization and more general manipulation of the
nuclear-spin density matrix through "state narrowing". These results
demonstrate the richness of this physical system and promise many new mysteries
for the future.
