Knowledge of the detailed structure of macromolecular interactions is key to a better understanding and modulation of essential cellular functions and pathological situations. Great efforts are invested in the development of improved computational prediction methods, including binding site prediction and protein-protein docking. These tools should benefit from the inclusion of evolutionary information, since the pressure to maintain functional interactions leads to conservation signals on protein surfaces at interacting sites and coevolution between contacting positions. However, unveiling such constraints and finding the best way to integrate them into computational pipelines remains a challenging area of research. Here, we first introduce evolutionary properties of interface structures, focusing on recent work exploring evolutionary mechanisms at play in protein interfaces and characterizing the complexity of evolutionary signals, such as interface deep mutational scans. Then, we review binding site predictors and interface structure modeling methods that integrate conservation and coevolution as important ingredients to improve predictive capacity, ending with a section dedicated to the prediction of binding modes between a globular protein domain and a short motif located within an intrinsically disordered or flexible region. Throughout the review, we discuss practical applications and recent promising developments, in particular regarding the use of coevolutionary information for interface structural prediction and the integration of these coevolution signals with machine learning and deep learning algorithms.