Traditional pedagogy has been transformed by the rapid adoption of artificial intelligence (AI), especially in student assessment. This paper reviews AI in education (AIEd), emphasizing Automated Essay Scoring (AES) and complex assignment assessment using Large Language Models (LLMs) and Natural Language Processing (NLP). The development of these technologies is examined, from early statistical models to contemporary Transformer-based architectures like Bidirectional Encoder Representations from Transformers (BERT) and Generative Pre-trained Transformers (GPT). Additionally, the benefits of AI-based grading, such as scalability and instant feedback, are critically evaluated against important drawbacks like algorithmic bias, explainability issues, and concerns about academic integrity. Lastly, future paths for human-AI cooperation in grading are suggested, arguing that AI should be utilized to complement human teachers rather than take their place.