Additive manufacturing (AM) of polymers and polymer composites is changing how customized, lightweight, and complex parts are produced across various industries. However, predicting the final properties of printed parts remains challenging due to variations in material compositions, processing conditions, and microstructural characteristics. This review explores how machine learning (ML) is being used to address these challenges. It examines the application of various ML approaches in polymer and polymer composite design for AM, including supervised, unsupervised, semi-supervised, self-supervised, and reinforcement learning, for predicting key properties such as mechanical strength, thermal stability, and electrical performance. The review also highlights hybrid techniques that combine ML with physics-informed modeling, including the use of digital twins, to enhance AM process control. Challenges and future perspectives, such as data scarcity, model interpretability, and computational demands, are discussed. In summary, ML is showing strong potential to support faster, more reliable, and more sustainable development of advanced polymers and polymer composites for AM.