Weak crossover (WCO) effects may be described as arising in a syntactic configuration where pronouns cannot be interpreted as co-construed with certain kinds of displaced or quantified antecedents. If it is correct to say that (i) the blocking of this co-construal does not seem logically required, (ii) the effect is syntactically conditioned, (iii) the effect is widespread in the world's languages, and (iv) it does not appear to arise from instruction, then it is reasonable to assume that the WCO effect is a peculiar consequence of the human language capacity and a clue to the structure of that capacity. This chapter reviews and compares the history and prospects of syntactic theories that have been proposed as accounting for weak crossover, while setting certain thresholds of what any explanatory theory should account for. Issues concern theories about the nature of binding relations, in particular the distinction between A- and A'-binding and bound variable interpretation, as well as attempts to reduce the WCO effect to principles that do not directly refer to the phenomenon. The role of c-command, of constraining vs. licensing conditions, syntactic and semantic dependency, obviation, and the distribution of effects (or non-effects) deemed related to WCO – such as weakest crossover, strong crossover, inverse linking, reconstruction, resumption, superiority, and functional readings of multiple quantifier sentences – are all considered. The explanatory force of several sorts of theories are explicated and compared.