The performance of symbolic inference tasks has long been a challenge to connectionists.In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule-based reasoning and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modelling.