Digital Twins (DTs) are becoming popular in Additive Manufacturing (AM) due to their ability to create virtual replicas of physical components of AM machines, which helps in real-time production monitoring. Advanced techniques such as Machine Learning (ML), Augmented Reality (AR), and simulation-based models play key roles in developing intelligent and adaptable DTs in manufacturing processes. However, questions remain regarding scalability, the integration of high-quality data, and the computational power required for real-time applications in developing DTs. Understanding the current state of DTs in AM is essential to address these challenges and fully utilize their potential in advancing AM processes. Considering this opportunity, this work aims to provide a comprehensive overview of DTs in AM by addressing the following four research questions: (1) What are the key types of DTs used in AM and their specific applications? (2) What are the recent developments and implementations of DTs? (3) How are DTs employed in process improvement and hybrid manufacturing? (4) How are DTs integrated with Industry 4.0 technologies? By discussing current applications and techniques, we aim to offer a better understanding and potential future research directions for researchers and practitioners in AM and DTs.