This is a brief survey of the use of transfinite induction in metric fixed‐point theory. Among the results discussed in some detail is the author′s 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi′s theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.