Abstract. In the 1960s, when population geneticists first began to collect data on the amount of genetic variation in natural populations, balancing selection was invoked as a possible explanation for how such high levels of molecular variation are maintained. However, the predictions of the neutral theory of molecular evolution have since become the standard by which cases of balancing selection may be inferred. Here we review the evidence for balancing selection acting on the major histocompatibility complex (MHC) of vertebrates, a genetic system that defies many of the predictions of neutrality. We apply many widely used tests of neutrality to MHC data as a benchmark for assessing the power of these tests. These tests can be categorized as detecting selection in the current generation, over the history of populations, or over the histories of species. We find that selection is not detectable in MHC datasets in every generation, population, or every evolutionary lineage. This suggests either that selection on the MHC is heterogeneous or that many of the current neutrality tests lack sufficient power to detect the selection consistently. Additionally, we identify a potential inference problem associated with several tests of neutrality. We demonstrate that the signals of selection may be generated in a relatively short period of microevolutionary time, yet these signals may take exceptionally long periods of time to be erased in the absence of selection. This is especially true for the neutrality test based on the ratio of nonsynonymous to synonymous substitutions. Inference of the nature of the selection events that create such signals should be approached with caution. However, a combination of tests on different time scales may overcome such problems.