This paper examines how various equating methods are affected by: (1) sampling error; (2) sample characteristics; and (3) characteristics of anchor test items. It reviews empirical studies that investigated the invariance of equating transformations, and it discusses empirical and simulation studies that focus on how the properties of anchor tests affect conventional and item response theory equating results. Rather than offering a cookbook procedure for obtaining accurate equating results, the paper provides some practical suggestions for practitioners to follow when equating and describes some needed research. More research is needed toward improving the use of analytic techniques for smoothing or modeling marginal and bivariate frequency distributions. More testing programs need to evaluate the extent to which their operational equating results are population invariant and to examine the similarity in equating results for major population subgroups taking the test forms at different administration dates. An investigation is needed of how lack of content representativeness of the linking items, or the differences in ability levels of the new and old form groups affect: (1) item parameter scaling and their interaction with the number of linking items, (2) the position of the linking items, and (3) the scaling procedure used. (LMO)