We argue that current theories of multisensory representations are inconsistent with the existence of a large proportion of multimodal neurons with gain fields and partially shifting receptive fields. Moreover, these theories do not fully resolve the recoding and statistical issues involved in multisensory integration. An alternative theory, which we have recently developed and review here, has important implications for the idea of 'frame of reference' in neural spatial representations. This theory is based on a neural architecture that combines basis functions and attractor dynamics. Basis function units are used to solve the recoding problem, whereas attractor dynamics are used for optimal statistical inferences. This architecture accounts for gain fields and partially shifting receptive fields, which emerge naturally as a result of the network connectivity and dynamics.