Intelligent systems of essay grading constitute important tools for educational technologies. They can significantly replace the manual scoring efforts and provide instructional feedback as well. These systems typically include two main parts: a feature extractor and an automatic grading model. The latter is generally based on computational and artificially intelligent methods. In this work, we focus on the feature extraction part. More precisely, we focus on argumentation and discourse-related features, which constitute high-level features. We discuss some state-of-the-art systems and analyze how argumentation and discourse analysis are used for extracting features and providing feedback.