Experimental kinetics of non-native protein aggregation are of practical importance in that they help dictate viable processing, formulation, and storage conditions for biotechnology products, and appear to play a role in determining the onset of a number of diseases. Fundamentally, aggregation kinetics provide insights into the identity of key intermediates in the process, and quantitative tests of available models of aggregation. Although aggregation kinetics often display seemingly disparate behaviors across different proteins and sample conditions, this review illustrates how many of these can be understood within a general framework that treats aggregation as a multi-stage process, and how most available kinetic models of aggregation can be grouped hierarchically in terms of which stage(s) they include. This provides an aid for workers seeking a mechanistic interpretation of in vitro aggregation kinetics, for discriminating among competing models, and in designing experiments to assess in vitro protein stability. Limitations and the utility of purely kinetic approaches to studying aggregation, clarifications of common misperceptions regarding experimental aggregation kinetics, and some outstanding challenges in the field are briefly discussed.