To achieve a full, theoretical understanding of a cognitive process, explanations of the process need to be provided at both symbolic (i.e., representational) and sub-symbolic levels of description. We argue that cognitive models implemented in vector-symbolic architectures (VSAs) intrinsically operate at both of levels and thus provide a needed bridge. We characterize the sub-symbolic level of VSAs in terms of a small set of linear algebra operations. We characterize the symbolic level of VSAs in terms of cognitive processes, in particular how information is represented, stored, and retrieved, and classify vector-symbolic cognitive models in the literature according to their implementation of these processes. On the basis of our analysis, we speculate on avenues for future research, and suggest means for theoretical unification of existent models.