  We review our theoretical work on the dynamics of a localized electron spin
interacting with an environment of nuclear spins. Our perturbative calculation
is valid for arbitrary polarization p of the nuclear spin system and arbitrary
nuclear spin I in a sufficiently large magnetic field. In general, the electron
spin shows rich dynamics, described by a sum of contributions with exponential
decay, non-exponential decay, and undamped oscillations. We have found an
abrupt crossover in the long-time spin dynamics at a critical shape and
dimensionality of the electron envelope wave function. We conclude with a
discussion of our proposed scheme to measure the relevant dynamics using a
standard spin-echo technique.
