  We review and summarize recent theoretical and experimental work on electron
spin dynamics in quantum dots and related nanostructures due to hyperfine
interaction with surrounding nuclear spins. This topic is of particular
interest with respect to several proposals for quantum information processing
in solid state systems. Specifically, we investigate the hyperfine interaction
of an electron spin confined in a quantum dot in an s-type conduction band with
the nuclear spins in the dot. This interaction is proportional to the square
modulus of the electron wave function at the location of each nucleus leading
to an inhomogeneous coupling, i.e. nuclei in different locations are coupled
with different strength. In the case of an initially fully polarized nuclear
spin system an exact analytical solution for the spin dynamics can be found.
For not completely polarized nuclei, approximation-free results can only be
obtained numerically in sufficiently small systems. We compare these exact
results with findings from several approximation strategies.
