Amyloid-related diseases are a group of illnesses in which an abnormal accumulation of proteins into fibrillar structures is evident. Results from a wide range of studies, ranging from identification of amyloid-β dimers in the brain to biophysical characterization of the interactions between amyloidogenic peptides and lipid membranes during fibril growth shed light on the initial events which take place during amyloid aggregation. Accounts of fibril disaggregation and formation of globular aggregates due to interactions with lipids or fatty acids further demonstrate the complexity of the aggregation process and the difficulty to treat amyloid-related diseases. There is an inherent difficulty in generalizing from studies of aggregation in vitro, but the involvement of too many cellular components limits the ability to follow amyloid aggregation in a cellular (or extracellular) context. Fortunately, the development of experimental methods to generate stable globular aggregates suggests new means of studying the molecular events associated with amyloid aggregation. Furthermore, simulation studies enable deeper understanding of the experimental results and provide useful predictions that can be tested in the laboratory. Computer simulations can nowadays provide molecular or even atomistic details that are experimentally not available or very difficult to obtain. In the present review, recent developments on modelling and experiments of amyloid aggregation are reviewed, and an integrative account on how isolated interactions (as observed in vitro and in silico) combine during the course of amyloid-related diseases is presented. Finally, it is argued that an integrative approach is necessary to get a better understanding of the protein aggregation process.