NLP models are imperfect and lack intricate capabilities that humans access automatically when processing speech or reading a text. Human language processing data can be leveraged to increase the performance of models and to pursue explanatory research for a better understanding of the differences between human and machine language processing. We review recent studies leveraging different types of cognitive processing signals, namely eye-tracking, M/EEG and fMRI data recorded during language understanding. We discuss the role of cognitive data for machine learning-based NLP methods and identify fundamental challenges for processing pipelines. Finally, we propose practical strategies for using these types of cognitive signals to enhance NLP models.