Skepticism regarding the tree model has a long tradition in historical linguistics. Although scholars have emphasized that the tree model and its long-standing counterpart, the wave theory, are not necessarily incompatible, the opinion that family trees are unrealistic and should be completely abandoned in the field of historical linguistics has always enjoyed a certain popularity. This skepticism has further increased with the advent of recently proposed techniques for data visualization which seem to confirm that we can study language history without trees. In this article, we show that the concrete arguments that have been brought up in favor of achronistic wave models do not hold. By comparing the phenomenon of incomplete lineage sorting in biology with processes in linguistics, we show that data which do not seem as though they can be explained using trees can indeed be explained without turning to diffusion as an explanation. At the same time, methodological limits in historical reconstruction might easily lead to an overestimation of regularity, which may in turn appear as conflicting patterns when the researcher is trying to reconstruct a coherent phylogeny. We illustrate how, in several instances, trees can benefit language comparison, although we also discuss their shortcomings in modeling mixed languages. While acknowledging that not all aspects of language history are tree-like, and that integrated models which capture both vertical and lateral language relations may depict language history more realistically than trees do, we conclude that all models claiming that vertical language relations can be completely ignored are essentially wrong: either they still tacitly draw upon family trees or they only provide a static display of data and thus fail to model temporal aspects of language history.