A central topic for linguistic theory is the degree to which the communicative function of language influences its form. In particular many so-called functional explanations argue that cross-linguistic constraints can be explained with reference to pressures imposed by processing. In apparent opposition to this is the innatist stance which claims that universals are properties imposed by an autonomous language module. This thesis approaches the issues raised by this conflict by examining the nature of the link between processing and universals. The starting point for the work, then, is not the discovery of new universals nor new explanations, but the question "exactly how do processing theories that have been proposed give rise to the universals that they claim to explain?" Careful investigation of this problem proves to be fruitful in highlighting the roles of innateness and function in explaining universals. The methodology chosen involves computational simulations of language as a complex adaptive system, in which language universals appear as emergent properties of the dynamics of the system and the influence of processing on use. This influence is characterised as a differential selection of competing variant forms. The simulation approach is first used to demonstrate the plausibility of a recent parsing explanation for word order universals. An extension of the model to deal with hierarchical universals relating to relative clauses leads to the conclusion that current explanations of hierarchies in general are incomplete. Instead, it is argued that implicational hierarchies are the result of competing processing pressures, in particular between morphological and parsing complexity. Further examination of relative clause processing and universals leads to an apparent flaw in the approach put forward. It is noted that not all processing pressures appear to show up as universals, challenging the explanatory adequacy of the functional explanations.