The successor representation has emerged as a powerful model for understanding the spatial coding properties of hippocampal place cells and entorhinal grid cells. However, the diverse, spatially-tuned cells of the primary output of hippocampal neurons - the subiculum - have eluded a unified account. Here, we demonstrate that incorporating rodent behavioural biases into the successor representation reproduces the heterogeneous activity patterns of subicular neurons. Notably, this framework accounts for boundary vector and corner cells; neuronal types that are absent from upstream hippocampal regions. Further, we show that subicular firing patterns are more accurately described by the successor representation than those of CA3/1 place cells when learnt over a basis set of hippocampal place fields. In our discussion, we present biologically plausible mechanisms by which this predictive framework could be learnt over appropriate timescales in subiculum. Collectively, this work offers the first unifying theory of subicular function that suggests that it, more so than other hippocampal regions, should be regarded as a predictive map of the environment.