The process of protein misfolding and aggregation has been associated with an increasing number of pathological conditions that include Alzheimer's and Parkinson's diseases, and type II diabetes. In addition, the discovery that proteins unrelated to any known disorder can be converted into aggregates of morphologies similar to those found in diseased tissue has lead to the recognition that this type of assemblies represents a generic state of polypeptide chains. Therefore, despite the enormous complexity of the in vivo mechanisms that have evolved in living organisms to prevent and control the formation of protein aggregates, the process of aggregation itself appears ultimately to be caused by intrinsic properties of polypeptide chains, in particular by the tendency of the backbone to form hydrogen bonds, and be modulated by the presence of specific patterns of hydrophobic and charged residues. Theoreticians have just recently started to respond to the challenge of identifying the determinants of the aggregation process. In this review, we provide an account of the theoretical results obtained so far.