It has been suggested that a change of nuclear shape may be described in terms of a phase transition and that specific nuclei may lie close to the critical point of the transition. Analytical descriptions of such critical‐point nuclei have been introduced recently and they are described briefly. The results of extensive searches for possible examples of critical‐point behavior are presented. Alternative pictures, such as describing bands in the candidate nuclei using simple ΔK=0 and ΔK=2 rotational‐coupling models, are discussed, and the limitations of the different approaches highlighted. A possible critical‐point description of the transition from a vibrational to rotational pairing phase is suggested.