Neural network based deep learning methods aim to learn representations of data and have produced state-of-the-art results in many natural language processing (NLP) tasks.Discourse parsing is an important research topic in discourse analysis,aiming to infer the discourse structure and model the coherence of a given text.This survey covers text-level discourse parsing,shallow discourse parsing and coherence assessment.We first introduce the basic concepts and traditional approaches,and then focus on recent advances in discourse structure oriented representation learning.We also introduce a trend of discourse structure aware representation learning that is to exploit discourse structures or discourse objectives for learning representations of sentences and documents for specific applications or for general purpose.Finally,we present a brief summary of the progress and discuss several future directions.