Inelastic neutron scattering, susceptibility, and high-field magnetization identify LiCuVO4 as a nearest-neighbour ferromagnetic, next-nearest-neighbour frustrated, quasi-onedimensional helimagnet, which is largely influenced by quantum fluctuations. Complementary band structure calculations provide a microscopic model with the correct sign and magnitude of the major exchange integrals.

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.