Despite massive sequencing efforts, understanding the difference between human pathogenic and benign variants remains a challenge. Computational variant effect predictors (VEPs) have emerged as essential tools for assessing the impact of genetic variants, although their performance varies. Initially, sequence-based methods dominated the field, but recent advances, particularly in protein structure prediction technologies like AlphaFold, have led to an increased utilization of structural information by VEPs aimed at scoring human missense variants. This review highlights the progress in integrating structural information into VEPs, showcasing novel models such as AlphaMissense, PrimateAI-3D, and CPT-1 that demonstrate improved variant evaluation. Structural data offers more interpretability, especially for non-loss-of-function variants, and provides insights into complex variant interactions in vivo. As the field advances, utilizing biomolecular complex structures will be pivotal for future VEP development, with recent breakthroughs in protein-ligand and protein-nucleic acid complex prediction offering new avenues.