Experiments have achieved a remarkable degree of quantum control of
states of a few electrons confined in gate-defined quantum dots. The
spin degree of freedom of the trapped electrons are promising building
blocks for quantum information processing. In these experiments the
environment of nuclear spins plays an important role in manipulating the
electronic states. I will present the experimental progress and the
associated theoretical description, in understanding the interplay of
dynamical nuclear polarization and spin-orbit interaction in GaAs double
quantum dots.