Elucidating the precise molecular events altered by disease-causing genetic variants represents a major challenge in translational bioinformatics. To this end, many studies have investigated the structural and functional impact of amino acid substitutions. Most of these studies were however limited in scope to either individual molecular functions or were concerned with functional effects (e.g. deleterious vs. neutral) without specifically considering possible molecular alterations. The recent growth of structural, molecular and genetic data presents an opportunity for more comprehensive studies to consider the structural environment of a residue of interest, to hypothesize specific molecular effects of sequence variants and to statistically associate these effects with genetic disease. In this study, we analyzed data sets of disease-causing and putatively neutral human variants mapped to protein 3D structures as part of a systematic study of the loss and gain of various types of functional attribute potentially underlying pathogenic molecular alterations. We first propose a formal model to assess probabilistically function-impacting variants. We then develop an array of structure-based functional residue predictors, evaluate their performance, and use them to quantify the impact of disease-causing amino acid substitutions on catalytic activity, metal binding, macromolecular binding, ligand binding, allosteric regulation and post-translational modifications. We show that our methodology generates actionable biological hypotheses for up to 41% of disease-causing genetic variants mapped to protein structures suggesting that it can be reliably used to guide experimental validation. Our results suggest that a significant fraction of disease-causing human variants mapping to protein structures are function-altering both in the presence and absence of stability disruption.