Self-supervised models of how the brain represents and categorises the causes of its sensory input can be divided into two classes: those that minimise the mutual information (i.e. redundancy) among evoked responses and those that minimise the prediction error. Although these models have similar goals, the way they are attained, and the functional architectures employed, can be fundamentally different. This review describes the two classes of models and their implications for the functional anatomy of sensory cortical hierarchies in the brain. We then consider how empirical evidence can be used to disambiguate between architectures that are sufficient for perceptual learning and synthesis. Most models of representational learning require prior assumptions about the distribution of sensory causes. Using the notion of empirical Bayes, we show that these assumptions are not necessary and that priors can be learned in a hierarchical context. Furthermore, we try to show that learning can be implemented in a biologically plausible way. The main point made in this review is that backward connections, mediating internal or generative models of how sensory inputs are caused, are essential if the process generating inputs cannot be inverted. Because these processes are dynamical in nature, sensory inputs correspond to a non-invertible nonlinear convolution of causes. This enforces an explicit parameterisation of generative models (i.e. backward connections) to enable approximate recognition and suggests that feedforward architectures, on their own, are not sufficient. Moreover, nonlinearities in generative models, that induce a dependence on backward connections, require these connections to be modulatory; so that estimated causes in higher cortical levels can interact to predict responses in lower levels. This is important in relation to functional asymmetries in forward and backward connections that have been demonstrated empirically. To ascertain whether backward influences are expressed functionally requires measurements of functional integration among brain systems. This review summarises approaches to integration in terms of effective connectivity and proceeds to address the question posed by the theoretical considerations above. In short, it will be shown that functional neuroimaging can be used to test for interactions between bottom-up and top-down inputs to an area. The conclusion of these studies points toward the prevalence of top-down influences and the plausibility of generative models of sensory brain function.