Although the mathematical principles underpinning population-level evolution are now well studied, the origin and evolution of morphological novelties has received far less attention. Here, a broad but general theory for how this sort of change takes place is outlined, relying on functional continuity, least-constrained components of morphology, redundancy and preadaptation. At least four distinct sorts of redundancy are identified: (i) redundancy arising through duplication (amplification); (ii) redundancy arising through regionalisation (parcellation); (iii) redundancy arising through functional convergence; and (iv) redundancy arising from shared function (functional degeneracy). Although organisms are here recognised to be functionally constrained ("burdened", in Riedl's terminology), these constraints can be overcome through the combination of the four principles given above. Contrary to its common treatment, functional constraint is neither an ever-increasing restriction on the scope of evolution, nor does it require drastic events to overcome or "break" it. Rather, it is an evolutionary quantity, subject to selection at some level. The rules that govern morphological evolution are the primary controls on what is allowed to happen in the evolution of the overall genotype-phenotype system, suggesting strong controls on the sorts of developmental changes that might be associated with macroevolution. This model, then, sees organism functionality as the primary control on evolvability, with exact genetic make-up being of secondary importance. It should prove possible to recast traditional notions of body-plan evolution into the formulations of complex system analysis, which in the future may prove a unifying discipline for fields as disparate as palaeontology and gene regulatory networks. In particular, understanding how morphology can evolve may provide the critical link between the ecological and morphological networks that are currently the intense focus of evolutionary investigations.