  The distinct distribution of local magnetic fields due to superconducting
vortices can be detected with nuclear magnetic resonance (NMR) and used to
investigate vortices and related physical properties of extreme type II
superconductivity. This review summarizes work on high temperature
superconductors (HTS) including cuprates and pnictide materials. Recent
experimental results are presented which reveal the nature of vortex matter and
novel electronic states. For example, the NMR spectrum has been found to
provide a sharp indication of the vortex melting transition. In the vortex
solid a frequency dependent spin-lattice relaxation has been reported in
cuprates, including YBa$_2$Cu$_3$O$_{7-x}$, Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$,
and Tl$_2$Ba$_2$CuO$_{6+\delta}$. These results have initiated a new
spectroscopy via Doppler shifted nodal quasiparticles for the investigation of
vortices. At very high magnetic fields this approach is a promising method for
the study of vortex core excitations. These measurements have been used to
quantify an induced spin density wave near the vortex cores in
Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$. Although the cuprates have a different
superconducting order parameter than the iron arsenide superconductors there
are, nonetheless, some striking similarities between them regarding vortex
dynamics and frequency dependent relaxation.
