Here we explore the history of unusual and uncommon isotopes of known elements on the periodic table. We discuss the (almost) true statement that all isotopes of an element react the same. Then we reach inside the atomic nucleus and hear of theories to describe nuclear structure and--hence--stability of various isotopes, beginning with Dmitri Ivanenko's work. We learn of the best model, shell structure, and its failings that appeared in the 1980s. Then we talk about half-lives, and how short ...