Fisher's exact test and Pearson's chi-square with continuity correction are frequently employed in the analysis of epidemiological data involving a 2 x 2 contingency table. This paper reviews the concepts and controversies underlying these procedures and discusses their appropriateness and adequacies in analyzing such data. Other related procedures such as unconditional exact tests and randomized and mid-p tests including some generalizations to a r x c table are also briefly reviewed.