Importance of the field-The advancement in material design and engineering has led to the rapid development of novel materials with increasing complexity and functions. Both non-degradable and degradable polymers have found wide applications in the controlled delivery field. Studies on drug release kinetics provide important information into the function of material systems. To elucidate the detailed transport mechanism and the structure-function relationship of a material system, it is critical to bridge the gap between the macroscopic data and the transport behavior at the molecular level.Areas covered in this review-The structure and function information of selected nondegradable and degradable polymers have been collected and summarized from literatures published after 1990s. The release kinetics of selected drug compounds from various material systems will be discussed in case studies. Recent progresses in the mathematical models based on different transport mechanisms will be highlighted.What the reader will gain-This article aims to provide an overview of structure-function relationships of selected non-degradable and degradable polymers as drug delivery matrices.Take home message-Understanding the structure-function relationship of the material system is key to the successful design of a delivery system for a particular application. Moreover, developing complex polymeric matrices requires more robust mathematical models to elucidate the solute transport mechanisms.