This review explores the application of Long Short-Term Memory (LSTM) networks, a specialized type of recurrent neural network (RNN), in the field of polymeric sciences. LSTM networks have shown notable effectiveness in modeling sequential data and predicting time-series outcomes, which are essential for understanding complex molecular structures and dynamic processes in polymers. This review delves into the use of LSTM models for predicting polymer properties, monitoring polymerization processes, and evaluating the degradation and mechanical performance of polymers. Additionally, it addresses the challenges related to data availability and interpretability. Through various case studies and comparative analyses, the review demonstrates the effectiveness of LSTM networks in different polymer science applications. Future directions are also discussed, with an emphasis on real-time applications and the need for interdisciplinary collaboration. The goal of this review is to connect advanced machine learning (ML) techniques with polymer science, thereby promoting innovation and improving predictive capabilities in the field.