This literature review studies the field of automated process extraction, i.e., transforming textual descriptions into structured processes using Natural Language Processing (NLP). We found that Machine Learning (ML) / Deep Learning (DL) methods are being increasingly used for the NLP component. In some cases, they were chosen for their suitability towards process extraction, and results show that they can outperform classic rule-based methods. We also found a paucity of gold-standard, scalable annotated datasets, which currently hinders objective evaluations as well as the training or fine-tuning of ML / DL methods. Finally, we discuss preliminary work on the application of LLMs for automated process extraction, as well as promising developments in this field.