Here we highlight an emerging trend in the use of machine learning classifiers to test for abstraction across patterns of neural activity. When a classifier algorithm is trained on data from one cognitive context, and tested on data from another, conclusions can be drawn about the role of a given brain region in representing information that abstracts across those cognitive contexts. We call this kind of analysis Multivariate Cross-Classification (MVCC), and review several domains where it has recently made an impact. MVCC has been important in establishing correspondences among neural patterns across cognitive domains, including motor-perception matching and cross-sensory matching. It has been used to test for similarity between neural patterns evoked by perception and those generated from memory. Other work has used MVCC to investigate the similarity of representations for semantic categories across different kinds of stimulus presentation, and in the presence of different cognitive demands. We use these examples to demonstrate the power of MVCC as a tool for investigating neural abstraction and discuss some important methodological issues related to its application.