The Immigration Reform and Control Act (IRCA) was passed in the closing days of the 1986 legislative session. The primary purpose of IRCA is to remove illegal aliens from the U.S. labor market. It has two primary policy instruments. One is granting legal status or amnesty for certain illegal aliens, thereby in part “wiping the slate clean.” The other is imposing penalties, referred to as employer sanctions, against employers who “knowingly” hire illegal aliens. Employer sanctions are intended to reduce the demand for illegal alien labor. The first sections of this paper develop an economic analysis of the illegal alien labor market, including the determinants of illegal migration and the impact on the economy. Then, that model is applied to the major provisions of IRCA and used to describe its likely consequences. A concluding section argues that because IRCA does not address the economic realities it is not likely to accomplish its objectives. The partial amnesty and impotent employer sanctions have not solved the illegal alien dilemma.