Amyloid proteins are linked to the pathogenesis of several diseases including Alzheimer’s disease, but at the same time a range of functional amyloids are physiologically important in humans. Although the disease pathogenies have been associated with protein aggregation, the mechanisms and factors that lead to protein aggregation are not completely understood. Paradoxically, unique characteristics of amyloids provide new opportunities for engineering innovative materials with biomedical applications. In this review, we discuss not only outstanding advances in biomedical applications of amyloid peptides, but also the mechanism of amyloid aggregation, factors affecting the process, and core sequences driving the aggregation. We aim with this review to provide a useful manual for those who engineer amyloids for innovative medicine solutions.