Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive "in vitro" measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics.