In this paper, we discuss amyloidogenic proteins, their misfolding, resulting structures, and interactions with membranes, which lead to membrane damage and subsequent cell death. Many of these proteins are implicated in serious illnesses such as Alzheimer's disease and Parkinson's disease. Misfolding of amyloidogenic proteins leads to the formation of polymorphic oligomers and fibrils. Oligomeric aggregates are widely thought to be the toxic species, however, fibrils also play a role in membrane damage. We focus on the structure of these aggregates and their interactions with model membranes. Study of interactions of amlyoidogenic proteins with model and natural membranes has shown the importance of the lipid bilayer in protein misfolding and aggregation and has led to the development of several models for membrane permeabilization by the resulting amyloid aggregates. We discuss several of these models: formation of structured pores by misfolded amyloidogenic proteins, extraction of lipids, interactions with receptors in biological membranes, and membrane destabilization by amyloid aggregates perhaps analogous to that caused by antimicrobial peptides.