Protein aggregation causes many devastating neurological and systemic diseases and represents a major problem in the preparation of recombinant proteins in biotechnology. Major advances in understanding the causes of this phenomenon have been made through the realisation that the analysis of the physico-chemical characteristics of the amino acids can provide accurate predictions about the rates of growth of the misfolded assemblies and the specific regions of the sequences that promote aggregation. More recently it has also been shown that the toxicity in vivo of protein aggregates can be predicted by estimating the propensity of polypeptide chains to form protofibrillar assemblies. In this tutorial review we describe the development of these predictions made through the Zyggregator method and the applications that have been explored so far.