How does the human brain represent meanings of words and pictures in terms of the underlying neural activity? This talk will present our research using machine learning methods together with fMRI brain imaging to study this question. One line of our research has involved training classifiers that identify which word a person is thinking about, based on their neural activity observed using fMRI. A more recent line involves developing a computational model that predicts the neural activity associated with arbitrary English words, including words for which we do not yet have brain image data. This computational model is trained using a combination of fMRI data associated with several dozen concrete nouns, together with statistics gathered from a trillion-word text corpus. Once trained, the model predicts fMRI activation for any other concrete noun appearing in the text corpus, with highly significant accuracies over the 60 nouns for which we currently have fMRI data.