The patterns of brain activation and functional connectivity, task-related and task-free, as a function of age have been well documented over the past 30 years. However, the aging brain undergoes structural changes that are likely to affect the functional properties of the brain. The relationship between brain structure and function started to be investigated more recently. Brain structure and brain function can influence behavioral outcomes independently, and several studies highlight independent contribution of structure and function on cognition. Here, a central assumption is that brain structure also affects behavior indirectly through its influence on brain function. In such a model, structure supports function. Although findings generally suggest that structure may indeed influence function, the direction of the associations, the variability in terms of regional effects and age windows when associations are observed vary greatly. Also, a certain number of studies highlight the independent contribution of structure and function on cognition. A critical aspect of studying aging is the necessity of longitudinal designs, allowing to observe true aging effects - as compared with age differences in cross-sectional designs. This review aims to give an updated account on research dealing with multimodal neuroimaging in aging, and more specifically on the links between structure and function and associated cognitive outcomes, putting in parallel findings from cross-sectional and longitudinal studies. Additionally, we discuss potential mechanisms by which age-related changes in structure may affect function, but also factors (sample characteristics, methodology) that may contribute to the heterogeneity of the findings and the lack of consensus on the associations between structure, function, cognition and aging.