Understanding the effects of genetic variation is a fundamental problem in biology that requires methods to analyse both physical and functional consequences of sequence changes at systems-wide and mechanistic scales. To achieve a systems view, protein interaction networks map which proteins physically interact, while genetic interaction networks inform on the phenotypic consequences of perturbing these protein interactions. Until recently, understanding the molecular mechanisms that underlie these interactions often required biophysical methods to determine the structures of the proteins involved. The past decade has seen the emergence of new approaches based on coevolution, deep mutational scanning and genome-scale genetic or chemical-genetic interaction mapping that enable modelling of the structures of individual proteins or protein complexes. Here, we review the emerging use of large-scale genetic datasets and deep learning approaches to model protein structures and their interactions, and discuss the integration of structural data from different sources.