Amyloid fibril formation is a process that represents an essential feature of the chemistry of proteins and plays a central role in human pathology and the biology of living organisms. In this Account, we shall describe some of the recent results on the sequence and structural determinants of protein aggregation. We shall describe the factors that govern aggregation of unfolded peptides and proteins. We shall then try to summarize the factors that pertain to the aggregation of partially structured states and will show that even fully folded states of proteins have an ability to aggregate into at least early oligomers with no need to undergo substantial conformational changes.