I will discuss recent advances in understanding the nuclear spin dynamics in low dimensional systems. The focus
will be on the hyperfine interaction between nuclear and electronic spins and the role this interaction plays on
the dynamical nuclear polarization of semiconductor nanostructures. I will address topics such as nuclear spin
relaxation time, nuclear spin polarization, and nuclear spin diffusion. As an example I will consider the case of
semiconductor quantum wells and discuss theoretical results in connection with experimental data.