Understanding how one brain region exerts influence over another in vivo is profoundly constrained by models used to infer or predict directed connectivity. Although such neural interactions rely on the anatomy of the brain, it remains unclear whether, at the macroscale, structural (or anatomical) connectivity provides useful constraints on models of directed connectivity. Here, we review the current state of research on this question, highlighting a key distinction between inference-based effective connectivity and prediction-based directed functional connectivity. We explore the methods via which structural connectivity has been integrated into directed connectivity models: through prior distributions, fixed parameters in state-space models and inputs to structure learning algorithms. Although the evidence suggests that integrating structural connectivity substantially improves directed connectivity models, assessments of reliability and out-of-sample validity are lacking. We conclude this Review with a strategy for future research that addresses current challenges and identifies opportunities for advancing the integration of structural and directed connectivity to ultimately improve understanding of the brain in health and disease.