A major challenge for systems neuroscience is to break the neural code. Computational algorithms for encoding information into neural activity and extracting information from measured activity afford understanding of how percepts, memories, thought, and knowledge are represented in patterns of brain activity. The past decade and a half has seen significant advances in the development of methods for decoding human neural activity, such as multivariate pattern classification, representational similarity analysis, hyperalignment, and stimulus-model-based encoding and decoding. This article reviews these advances and integrates neural decoding methods into a common framework organized around the concept of high-dimensional representational spaces.