Discourse comprehension requires the capacity to store referents in memory and to subsequently retrieve them when appropriate. The linguistic, psycholinguistic and neuroscientific theories of reference comprehension can roughly be divided into two coarse-grained computational frameworks: connectionism and symbolism. We propose a computationally efficient and neurobiologically plausible computational model of reference comprehension that synthesises these two frameworks: the bundle memory model. We show that this model can perform reference comprehension by having it read sentences containing one or more referents and answer comprehension questions about them. By lesioning either the connectionist or the symbolic parts of the model we show that the frameworks complement each other and that combining them leads to capacities unavailable to either framework alone. Moreover, we trained several recurrent neural networks to perform reference comprehension, which were initially intended as simple control models. Unexpectedly, some of these models performed just as well as the bundle memory model and showed behaviours which many (psycho)linguists believe such models should not be able to do. Both the bundle memory model and the recurrent neural networks may provide fresh hypotheses on how the brain could perform reference comprehension.