After the discovery of high temperature superconductivity in a family of Cu oxides, the search for exotic phases of matter in strongly correlated electron systems has become an independent and extremely active field of research in Condensed Matter Physics. In that respect, frustrated quantum magnets play a central role: Their description naturally leads to some of the minimal models to which a large part of the theoretical activity is devoted, such as the quantum dimer model or models of hard-core bosons on a lattice. In parallel, the synthesis of new compounds allows fruitful interactions with experimentalists, with the hope to observe some of the phases believed to be realized in these models. In this talk, I will discuss three specific examples of exotic phases (quadrupolar order, supersolid phases and Resonating Valence Bond phases) that have recently been proposed to account for the properties of some Cu and Ni compounds.