Strong electron correlation lies at the root of many quantum collective phenomena observed in solids, including high Tc superconductivity. Theoretically, the problem of many interacting electrons is difficult to treat, however, and a microscopic understanding of strongly correlated systems remains one of the foremost challenges in modern physics. A particularly clean realisation of this general problem is found in magnetic systems, where theory and experiment are both well developed and complementary. The role of the chemist in this endeavour is to provide model experimental systems to both inspire new developments in theory and to confirm existing predictions. This thesis aims to demonstrate aspects of both synthesis and physical characterisation of such model systems, with particular emphasis on materials which exhibit unusual quantum ground states due to a combination of reduced dimensionality, low spin, and geometric frustration. Four materials are considered: The first among these is a new material, KTi(SO4)2·(H2O), which was prepared using a hydrothermal route, and characterised by magnetic susceptibility, specific heat, and high field magnetisation measurements. Fitting exact diagonalisation and series expansion results to these data imply that KTi(SO4)2·(H2O)is a long-sought experimental realization of the S = 1/2 Heisenberg frustrated (J1 − J2) chain model in the dimerised regime of the phase diagram. The anhydrous analogue of KTi(SO4)2·(H2O), KTi(SO4)2, was also investigated, and found by magnetic neutron scattering to exemplify the S = 1/2 Heisenberg anisotropic triangular lattice model in the 1D chain limit. The final two materials discussed are the naturally occurring minerals volborthite and herbertsmithite, both thought to realise the S = 1/2 Heisenberg kagome antiferromagnet model. Diffuse and inelastic magnetic neutron scattering experiments, however, indicate that the kagome physics are partially destroyed by defects in the former and lattice distortion in the latter.