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Polymeric membranes have become essential for energy-efficient gas separations such as natural gas sweetening, hydrogen separation, and carbon dioxide capture. Polymeric membranes face challenges like permeability-selectivity tradeoffs, plasticization, and physical aging, limiting their broader applicability. Machine learning (ML) techniques are increasingly used to address these challenges. This review covers current ML applications in polymeric gas separation membrane design, focusing on three key components: polymer data, representation methods, and ML algorithms. Exploring diverse polymer datasets related to gas separation, encompassing experimental, computational, and synthetic data, forms the foundation of ML applications. Various polymer representation methods are discussed, ranging from traditional descriptors and fingerprints to deep learning-based embeddings. Furthermore, we examine diverse ML algorithms applied to gas separation polymers. It provides insights into fundamental concepts such as supervised and unsupervised learning, emphasizing their applications in the context of polymer membranes. The review also extends to advanced ML techniques, including data-centric and model-centric methods, aimed at addressing challenges unique to polymer membranes, focusing on accurate screening and inverse design.