Neural networks models for NLP are typically implemented without the explicit encoding of language rules and yet they are able to break one performance record after another. This has generated a lot of research interest in interpreting the representations learned by these networks. We propose here a novel interpretation approach that relies on the only processing system we have that does understand language: the human brain. We use brain imaging recordings of subjects reading complex natural text to interpret word and sequence embeddings from 4 recent NLP models - ELMo, USE, BERT and Transformer-XL. We study how their representations differ across layer depth, context length, and attention type. Our results reveal differences in the context-related representations across these models. Further, in the transformer models, we find an interaction between layer depth and context length, and between layer depth and attention type. We finally hypothesize that altering BERT to better align with brain recordings would enable it to also better understand language. Probing the altered BERT using syntactic NLP tasks reveals that the model with increased brain-alignment outperforms the original model. Cognitive neuroscientists have already begun using NLP networks to study the brain, and this work closes the loop to allow the interaction between NLP and cognitive neuroscience to be a true cross-pollination.