The current status of item response theory (IRT) is discussed. Several IRT methods exist for assessing whether an item is biased. Focus is on methods proposed by L. M. Rudner (1975), F. M. Lord (1977), D. Thissen et al. (1988) and R. L. Linn and D. Harnisch (1981). Rudner suggested a measure of the area lying between the two item characteristic curves (ICCs). Both signed and unsigned indices have been suggested, which may differ where the ICCs cross. Lord proposed asymptotic chi square tests for the equality of the "a" and "b" parameters as well as tests for each of these parameters separately. Thissen has more recently suggested a successive model fitting procedure where models to be tested can include those that constrain one or more of the three parameters for an item to be equal for two groups. The method developed by Linn and Harnisch calibrates the item only for the total group; the observed performance of the focal group is then compared to that expected from the IRT model. Issues raised by these methods are related to accuracy of item calibration, effects of estimation error, the problem of widely different ability distributions, goodness of fit, and problems associated with tests that are somewhat speeded or with data sets with many omits such as may occur on difficult tests under formula scoring instructions. Recent uses of parameter estimation methods based on marginal maximum likelihood methods using the BILOG program are discussed briefly. (TJH)