On the Balance of Unrooted Trees Mareike Fischer and Volkmar Liebscher Vol. 25, no. 1, pp. 133-150, 2021. Regular paper. Abstract We solve a class of optimization problems for (phylogenetic) $X$-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so far these problems have not been characterized and solved in a systematic way. In this work we generalize the concept and also present several applications. Moreover, our results give rise to a nice notion of balance for trees, which plays an important role in various different research areas, including mathematical phylogenetics as well as computer science. Unsurprisingly, so-called caterpillars are the most unbalanced tree shapes, but it turns out that balanced tree shapes cannot be described so easily as they need not even be unique.  This work is licensed under the terms of the CC-BY license. Submitted: March 2019. Reviewed: July 2019. Revised: October 2020. Accepted: January 2021. Final: January 2021. Published: January 2021. Communicated by Giuseppe Liotta article (PDF) BibTeX