Knee cartilage and meniscus have important roles in supporting loading in the knee, and their functional ability to support these loads is in large part due to their structure. Degeneration of these tissues through the process of aging, traumatic injury, and diseases like osteoarthritis can drastically change the structure and function of knee cartilage and meniscus. Because the structure and function of cartilage and meniscus are inherently linked, changes in one impact the other. To evaluate the effects of changes in functional loading of cartilage on its structure, non-invasive medical imaging techniques were used to analyze pre- and post-run scans to look for post-exercise changes in the quantitative magnetic resonance imaging parameter T2 relaxation time to better design future studies monitoring cartilage health. To evaluate the effects of changes in cartilage and meniscus structure on their function, mechanical testing techniques were used to examine the specific use case of the impact of imaging contrast agent solution exposure on meniscus and cartilage structure to develop a road map for designing safer contrast agent solutions. Finally, a combination of function and structural measurements were leveraged to characterize material properties of previously understudied pediatric meniscus specimens. Insights from this line of investigation will inform future studies focused on developing treatments and therapies targeted specifically for pediatric meniscus tissue. The work presented in this thesis advances our scientific understanding of the structure-function relationship of knee cartilage and meniscus and will provide a foundation for research supporting the development of treatments, interventions, and therapies for injury and disease in the knee for people of all ages.