One of the main limitations of scalability in body-brain evolution systems is the representation chosen for encoding creatures. This paper defines a class of representations called generative representations, which are identified by their ability to reuse elements of the genotype in the translation to the phenotype. This paper presents an example of a generative representation for the concurrent evolution of the morphology and neural controller of simulated robots, and also introduces GENRE, an evolutionary system for evolving designs using this representation. Applying GENRE to the task of evolving robots for locomotion and comparing it against a non-generative (direct) representation shows that the generative representation system rapidly produces robots with significantly greater fitness. Analyzing these results shows that the generative representation system achieves better performance by capturing useful bias from the design space and by allowing viable large scale mutations in the phenotype. Generative representations thereby enable the encapsulation, coordination, and reuse of assemblies of parts.