  Quantum magnets represent an ideal playground for the controlled realization
of novel quantum phases and of quantum phase transitions. The Hamiltonian of
the system can be indeed manipulated by applying a magnetic field or pressure
on the sample. When doping the system with non-magnetic impurities, novel
inhomogeneous phases emerge from the interplay between geometric randomness and
quantum fluctuations. In this paper we review our recent work on quantum phase
transitions and novel quantum phases realized in disordered quantum magnets.
The system inhomogeneity is found to strongly affect phase transitions by
changing their universality class, giving the transition a novel, quantum
percolative nature. Such transitions connect conventionally ordered phases to
unconventional, quantum disordered ones - quantum Griffiths phases, magnetic
Bose glass phases - exhibiting gapless spectra associated with low-energy
localized excitations.
