What is Renormalization?

"Preprint" of paper from 1989 that wasn't arxiv'ed at the time. Abstract: Our understanding of quantum field theories, and, in particular, of renomalization has changed radically in recent years; renormalization is no longer a deeply mysterious procedure for hiding embarrassing infinities. This talk is a non-technical presentation of modern attitudes towards renormalization, and their implications (both theoretical and experimental) for quantum theories of electromagnetic, strong, and weak interactions.