Research into immigration has for many years focused most of its attention on the issue of how immigrants adapt to host societies. This tendency is especially true in the work of sociologists. Yet if we acknowledge the growing ethnic diversity today in the United States and elsewhere, the most interesting questions arise as to how immigrants influence the host society--not how they adapt to it. This paper proposes a sociological theory to account for such influence. For evidence it draws on a variety of empirical examples from research on ethnic communities in the United States.