The conversion of proteins from their soluble states into well-organized fibrillar aggregates is associated with a wide range of pathological conditions, including neurodegenerative diseases and systemic amyloidoses. In this review, we discuss the mechanism of aggregation of globular proteins under conditions in which they are initially folded. Although a conformational change of the native state is generally necessary to initiate aggregation, we show that a transition across the major energy barrier for unfolding is not essential and that aggregation may well be initiated from locally unfolded states that become accessible, for example, via thermal fluctuations occurring under physiological conditions. We review recent evidence on this topic and discuss its significance for understanding the onset and potential inhibition of protein aggregation in the context of diseases.