The formation of macroscopic biofilaments from monomeric peptides is a process central to both normal and disease biology, and a very active area of research. An example of particular significance is the formation of amyloid plaques from normally soluble proteins in several neurodegenerative conditions including Alzheimer’s disease. Traditionally, attention has focused on the proliferation of macroscopic quantities of biofilaments, and experimentalists have relied on bulk measurements to quantify this. By contrast, the initiation of the aggregation reaction has been comparatively understudied, despite the involvement of oligomeric intermediates that are considered to be the key pathogenic agents in many amyloidogenic diseases. This is due in large part to the key quantities measured in bulk experiments being insensitive to the details of the initiation step, and to the difficulties faced until recently in detecting comparatively rare oligomeric species. In this thesis I describe a number of theoretical approaches towards filling this crucial gap in our knowledge. These approaches fall into 3 main themes: modelling the early stages of bulk aggregation kinetics in greater detail; developing general kinetic theories of filament formation via initial oligomeric intermediates; and investigating heterogeneity within oligomer populations using equilibrium statistical mechanical modelling. In several instances I have already been able to apply these theories to experimental results, furthering our practical understanding of these processes in vitro. A final chapter is devoted to a highly general and insightful theoretical method for developing analytical solutions for the kinetics of a wide range of self-assembly phenomena. Although not focused on early events in amyloid aggregation, it is already finding application in this field, as in many others.