Minimum competency testing, in which passing a uniform test is necessary (but not sufficient) for promotion or graduation, has been carried out in a number of colleges, including the City University of New York (CUNY). Competency programs usually have three basic components: placement testing, remedial instruction, and exit testing. Competency testing at the high school level is typically mandated on a statewide basis. At the college level, there is also a trend toward systemwide programs, particularly in open admissions schools. Most competency programs in both the high schools and colleges test traditional basic skills: reading, writing, math, and particularly at the college level, elementary algebra. Information is presented on testing programs at CUNY, public colleges of New Jersey, and the university system of Georgia. The extent to which math competency tests should stress conventional arithmetic is a matter of controversy. Although there is public support for competency testing, it has been criticized on the basis of the test content, which in some programs has been characterized as culturally biased and therefore discriminatory. Other criticisms have been directed to the level of difficulty of the tests, the neglect of the rest of the curriculum because of the emphasis on basic skills, and the need to base assessment on teachers' perceptions as well as test scores. (SW)