In this chapter, we present an overview of the kinetics and thermodynamics of protein aggregation into amyloid fibrils. The perspective we adopt is largely experimental, but we also discuss recent developments in data analysis and we show that only a combination of well-designed experiments with appropriate theoretical modelling is able to provide detailed mechanistic insight into the complex pathways of amyloid formation. In the first part of the chapter, we describe measurements of the thermodynamic stability of the amyloid state with respect to the soluble state of proteins, as well as the magnitude and origin of this stability. In the second part, we discuss in detail the kinetics of the individual molecular steps in the overall mechanism of the conversion of soluble protein into amyloid fibrils. Finally, we highlight the effects of external factors, such as salt type and concentration, chemical denaturants and molecular chaperones on the kinetics of aggregation.