Geometric magnetic frustration is a phenomenon that arises through the competing exchange interactions that occur due to the arrangement of magnetic ions within the crystal structure of a material. In this work, the structural and magnetic behaviour of inorganic and hybrid systems that contain a triangular or kagomé arrangement of ions is explored through the complementary use of powder diffraction, magnetometry, heat capacity and muon spectroscopy measurements. The first series of materials reported are the mineral barlowite, Cu4(OH)6FBr, and its halide analogues, Cu4(OH)6FCl and Cu4(OH)6FI. Each of these systems contain a kagomé network of Cu2+ ions which are separated by an additional Cu2+ site. At room temperature, the crystal structures belong to the P63/mmc hexagonal space group, where the interlayer Cu2+ is disordered. Upon cooling, a structural transition takes place to varying extents across the series, in which the average structure can be described by the orthorhombic P nma space group. However, some remaining disorder on the interlayer site is unearthed, which can be correlated to features observed in the magnetic behaviour across this series. Next, the magnetic behaviour of the Zn-barlowite series, ZnxCu4-x(OH)6FBr, is investigated using neutron powder diffraction, magnetometry and muon spectroscopy techniques. There is evidence to suggest that Zn2+ preferentially occupies the interlayer Cu2+ site, which magnetically decouples the kagomé layers from each other. This is shown via muon spin relaxation measurements, alongside supporting DFT muon-site calculations, that provide evidence for fluctuating magnetic moments in highly-substituted samples at sub-kelvin temperatures. This behaviour is indicative of the presence of a dynamic magnetic ground state such as that associated with the elusive quantum spin liquid. The family of metal-organic frameworks with the formula Cu3(CO3)2(X )3 ·2ClO4 are formed from kagomé layers that are separated by an organic linker, X = 1,2- bis(4-pyridyl)ethane, 1,2-bis(4-pyridyl)ethylene or 4,4'-azopyridine. A new crystal structure with the space group P3 is proposed for these systems, which adequately describes the disorder present in the organic linkers. Through characterisation via magnetic susceptibility, heat capacity and powder diffraction measurements, the magnetic structures of these systems suggest that antiferromagnetic exchange occurs through these linkers. Meanwhile, the nature of the exchange within the kagomé layers is predicted to be ferromagnetic rather than antiferromagnetic. KFe(C2O4)F is a hybrid coordination framework containing a distorted triangular arrangement of Fe2+ ions that are bound through oxalate linkers. A comprehensive neutron powder diffraction and muon spectroscopy study reveals that the magnetic structure of this material contains quasi-one-dimensional Fe–F–Fe chains that are antiferromagnetically coupled, suggesting that a combination of low-dimensionality and magnetic frustration characterises the magnetic ground state of this system.