Interplay between strong correlations and frustrated geometry offers a generic recipe for experimentalists and theorists searching for materials exhibiting exotic ground-states and unconventional phase transitions which might lead to unsuspected applications. The project describes in details several promising routes to achieve the double goal of i) understanding the novel physical concepts at play and ii) providing a quantitative understanding of the related microscopic models hence opening the way to material design. The project focuses more explicitly on frustrated quantum magnets, itinerant correlated particles (electrons or bosons) on frustrated geometries and on systems with emerging excitations carrying non-abelian statistics (as in some novel fractional Quantum Hall states). One common feature of such systems is the potential emergence of exotic topological properties of its ground-state (useful e.g. to build a "quantum computor") due to its constrained nature linked to very strong correlations.