<p>Many patterns of phenotypic evolution are described and analyzed from a phenotype space perspective. In most instantiations of phenotype space, the set of phenotypic variants is endowed with a metric structure derived from some measure of geometric, anatomical, or structural similarity among variants: a notion of phenotypic distance is defined and phenotypic variants are spatially organized accordingly. While these approaches are successful in addressing many biological questions, metric topologies so defined are limited in their ability to shed mechanistic light on phenotypic evolution, because they do not embody in their definition the processes underlying the phenotype’s variability. Building on results from theoretical biochemistry and phenotype landscape theory, it is proposed to complement this default metric structure with an additional structure that considers the factors involved in the expression of the phenotype of interest. This shift in perspective leads to a genetic or developmental representation of the phenotype from which emerges a notion of evolutionary accessibility among phenotypic variants. We illustrate how accessibility structure strengthens the explanatory power of phenotype space by helping characterize constraints on variation and how these constraints may interfere or align with external selective pressures in the course of phenotypic evolution.</p>