The design and development of polymeric materials have been a hot domain for decades. However, traditional experiments and molecular simulations are time-consuming and labor-intensive, which no longer meet the requirements of new materials development. With the rapid advances of artificial intelligence and materials informatics, machine learning algorithms are increasingly applied in materials science, aiming to shorten the development period of new materials. With the evolution of polymeric materials, the structure of polymers has become more and more complex. Traditional machine learning algorithms often do not perform satisfactorily when dealing with complex data. Presently, deep learning algorithms, including deep neural networks, convolutional neural networks, generative adversarial networks, recurrent neural networks, and graph neural networks, show their uniquely excellent learning capabilities for large and complex data, which will be a powerful tool for the design and development of polymeric materials. This Review introduces principles of several currently popular deep learning algorithms and discusses their multiple applications in the materials field. Applications range from property prediction and molecular generation at the molecular level to structure identification and material synthesis in polymers. Finally, future challenges and opportunities for the application of deep learning in polymeric materials are discussed.