Large Language Models (LLMs) excel in various natural language tasks but often struggle with long-horizon planning problems requiring structured reasoning. This limitation has drawn interest in integrating neuro-symbolic approaches within the Automated Planning (AP) and Natural Language Processing (NLP) communities. However, identifying optimal AP deployment frameworks can be daunting. This paper aims to provide a timely survey of the current research with an in-depth analysis, positioning LLMs as tools for extracting and refining planning models to support reliable AP planners. By systematically reviewing the current state of research, we highlight methodologies, and identify critical challenges and future directions, hoping to contribute to the joint research on NLP and Automated Planning.