  In this review, we describe the potentialities offered by the nuclear
magnetic resonance (NMR) technique to explore at a microscopic level new
quantum states of condensed matter induced by high magnetic fields. We focus on
experiments realised in resistive (up to 34~T) or hybrid (up to 45~T) magnets,
which open a large access to these quantum phase transitions. After an
introduction on NMR observable, we consider several topics: quantum spin
systems (spin-Peierls transition, spin ladders, spin nematic phases,
magnetisation plateaus and Bose-Einstein condensation of triplet excitations),
the field-induced charge density wave (CDW) in high $T_c$~superconductors, and
exotic superconductivity including the Fulde-Ferrel-Larkin-Ovchinnikov
superconducting state and the field-induced superconductivity due to the
Jaccarino-Peter mechanism.
