Efforts to explain human and animal vision, and to automate visual function in machines, have found it difficult to account for the view-invariant perception of universals such as environmental objects or processes, and the explicit perception of featural parts and wholes in visual scenes. A handful of unsupservised learning methods, many of which relate directly to independent components analysis (ICA), have been used to make predictive perceptual models of the spatial and temporal statistical structure in natural visual scenes, and to develop principled explanations for several important properties of the architecture and dynamics of mammalian visual cortex. Emerging principles include a new understanding of invariances and part-whole compositions in terms of the hierarchical analysis of covariation in feature subspaces, reminiscent of the processing across layers and areas of visual cortex, and the analysis of view manifolds, which relate to the topologically ordered feature maps in cortex.