The tendency to discretize biology permeates taxonomy and systematics, leading to models that simplify the often continuous nature of populations. Even when the assumption of panmixia is relaxed, most models still assume some degree of discrete structure. The multispecies coalescent has emerged as a powerful model in phylogenetics, but in its common implementation is entirely space-independent – what we call the “missingz-axis”. In this article, we review the many lines of evidence for how continuous spatial structure can impact phylogenetic inference. We illustrate and expand on these by using complex continuous-space demographic models that include distinct modes of speciation. We find that the impact of spatial structure permeates all aspects of phylogenetic inference, including gene tree stoichiometry, topological and branch-length variance, network estimation, and species delimitation. We conclude by utilizing our results to suggest how researchers can identify spatial structure in phylogenetic datasets.