The misfolding and aggregation of proteins is closely associated with more than fifty human disorders, including Alzheimer's and Parkinson's diseases, all of which are currently incurable and many represent a major threat to human life. The mechanism of protein aggregation is subject to extensive studies. The damaging effects associated with protein aggregation have been attributed to amyloidogenic species that are present during the misfolding process. In particular, oligomeric species are, however, intrinsically difficult to study as a consequence of their low abundance and highly heterogeneous nature. The first chapter of my thesis gives an introduction into the field of protein folding and misfolding with a focus on the study of protein aggregation, and toxic effects relevant to human disorders. The second chapter of my thesis describes the development of a methodology that enables the study of aggregate induced lipid bilayer permeability, possibly the most general mechanism of protein aggregate toxicity. Surface-tethered lipid vesicles functioning as optochemical probes sensitive to membrane integrity are imaged using total internal reflection microscopy. It is shown that oligomeric species of the 42-residue form of the A$\beta$ peptide (A$\beta$42) are responsible for the membrane disruption. The methodology can be applied to the study of other proteins such as $\alpha$-synuclein and tau, and the ability of antibodies and chaperones to counteract the aggregate induced lipid bilayer permeability can be assessed. Furthermore, lipid bilayer permeability induced by aggregates formed in human induced pluripotent stem cells can be studied. The third chapter presents a new approach for the measurement of protein aggregation kinetics by following the development of the lipid bilayer permeability over the course of the aggregation process of A$\beta$42. The aggregation kinetics can be modulated with molecular chaperones and pre-formed seed fibrils, which allows secondary nucleation to be identified as the process that drives the formation of species responsible for the lipid bilayer permeability. The fourth chapter describes the development of a three-pronged strategy to study the mechanism of $\alpha$-synuclein amyloid formation. The aggregation is studied in the presence of lipid vesicles or pre-formed fibrils at neutral or acidic pH of the solution. The influence of single-point mutations on the aggregation of $\alpha$-synuclein is described. Furthermore, the strategy is applied to the characterisation of the ability of antibodies and small molecules to inhibit the aggregation, and thus has the potential for the development of therapeutical agents. The work presented in the fifth chapter characterises the amyloid fibril populations formed by $\alpha$-synuclein and mutational variants associated with familial Parkinson's disease. X-ray crystallography, circular dichroism spectroscopy, Fourier transform infrared spectroscopy, transmission electron microscopy and atomic force microscopy have all been applied to the analysis of these amyloid fibrils. Finally, the sixth chapter summarises the results described in this thesis and points out future opportunities in the context of fundamental and translational studies related to the research area of protein misfolding disorders.