What are some good survey or review papers on the state of the art of machine learning approaches to grammatical/syntactic structure of natural languages?
“Grammar as a foreign language” (2015) by Vinyals et al. is not a review paper but is a significant breakthrough by applying sequence-to-sequence deep learning.
"Advances in natural language processing" (2015) by Hirschberg and Manning provides a general overview, including parsing.
"Recent Trends in Deep Learning Based Natural Language Processing" (2018) by Young et al. covers popular deep learning approaches and lists current benchmarks for parsing.