Polyhedral clusters containing boron, alone or in combination with other elements, have been known for nearly a century, and intensive studies of their structures, bonding, and reactivity have been under way for more than half that period; yet interest and practical applications in this area continue to grow. Two main reasons can be identified for this attention: the three-dimensional delocalized bonding that confers exceptional stability in these clusters is now recognized to have broad significance for deepening our understanding of covalent bonding, with implications for both organic and inorganic chemistry; secondly, many of the special properties of boron clusters are uniquely suited to specific applications. This article attempts to summarize the current state of the art, illustrated by examples selected to convey some of the excitement and possibilities for future exploitation of these remarkable compounds.