Until the 1970s, there were few signs of change in the historic difference of one standard deviation between average ability or achievement test scores of black and white students. From 1970 to the mid-to-late 1980s, there was a substantial convergence of the average achievement test scores of blacks and whites. From the mid-to-late 1980s to 1992, test scores began to diverge again. This paper reviews evidence about the timing of the change in test scores and the types of tests in which it has occurred. It mainly uses National Assessment of Educational Progress data, though the convergence appears in other test series. Herrnstein and Murray's "The Bell Curve" stands almost alone in minimizing the importance of the convergent trends. A longer-term convergence between the verbal abilities of blacks and whites is seen in General Social Survey (GSS) data. GSS data shows a long-term decline in verbal ability among whites. Black-white differences in cognitive tests appear to have been reduced for cohorts born after the mid-1960s. The paper stresses the importance of the many cognitive tests across which black performance has begun to converge toward that of whites. (Contains 60 references.) (SM)