Human brains differ in their structural and functional organization across individuals. There is a long history of trying to relate either structural or functional brain features to human aspects, such as behavioral and cognitive variables. However, more recently, increasing attention has been drawn to the problem of understanding how brain structure and function are related to each other. In this talk, we introduce a statistical framework that jointly models brain structure and function. We adopt a Riemannian modeling approach to account for the non-Euclidean geometry of these complex traits and embed a random-effects component in order to disentangle genetic sources of variability from those driven by unique environmental factors. We then apply the proposed model to the Human Connectome Project dataset to explore spontaneous co-variation between brain shape and connectivity in young healthy individuals.