Recently, there has been much experimental progress in the search for new quantum paramagnetic phases of matter though successful fabrication of frustrated spin 1/2 magnets. In this talk, I will focus on two such materials: the three-dimensional "hyper-kagome" lattice system Na₄Ir₃O₈ (NIO) and a quasi-two-dimensional family of layered kagome lattice systems dubbed "Zn-paratacamite". Both NIO and fully doped Zn-paratacamite show no sign of magnetic order down to the lowest temperatures studied and hence are considered candidate systems for hosting a quantum spin liquid phase. Regarding NIO, I will discuss a few scenarios for a spin liquid phase in addition to possible magnetic ordering, should it arise at very low temperatures.

Concerning Zn-paratacamite, I will argue that the Neel and valence- bond-solid phases in the experimentally observed rich phase diagram arise from structural distortion induced by doping. Lastly, for both materials I will present predictions for future X-ray and inelastic neutron scattering experiments which can test our theories.