Machine learning is increasingly being applied in polymer chemistry to link chemical structures to macroscopic properties of polymers and to identify chemical patterns in the polymer structures that help improve specific properties. To facilitate this, a chemical dataset needs to be translated into machine readable descriptors. However, limited and inadequately curated datasets, broad molecular weight distributions, and irregular polymer configurations pose significant challenges. Most off the shelf mathematical models often need refinement for specific applications. Addressing these challenges demand a close collaboration between chemists and mathematicians as chemists must formulate research questions in mathematical terms while mathematicians are required to refine models for specific applications. This review unites both disciplines to address dataset curation hurdles and highlight advances in polymer synthesis and modeling that enhance data availability. It then surveys ML approaches used to predict solid-state properties, solution behavior, composite performance, and emerging applications such as drug delivery and the polymer-biology interface. A perspective of the field is concluded and the importance of FAIR (findability, accessibility, interoperability, and reusability) data and the integration of polymer theory and data are discussed, and the thoughts on the machine-human interface are shared.