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.
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