Volatile sulfur compounds (VSCs), particularly low molecular weight sulfhydryls like hydrogen sulfide (H2S) and methanethiol (MeSH), are often observed in wines with sulfurous off-aromas. Recent work has shown both H2S and MeSH can increase up to a few µM (> 40 µg/L) during anoxic storage, but the identity of the latent sources of these sulfhydryls is still disputed. This review critically evaluates the latent precursors and pathways likely to be responsible for the loss and formation of these sulfhydryls during wine storage based on the existing enology literature as well as studies from food chemistry, geochemistry, biochemistry, and synthetic chemistry. We propose that three precursor classes have sufficient concentration and metastability to serve as latent sulfhydryl precursors in wine: 1) transition metal-sulfhydryl complexes, particularly those formed following Cu(II) addition, which are released under anoxic conditions through an unknown mechanism; 2) asymmetric disulfides, polysulfanes, and (di)organopolysulfanes formed through transition-metal mediated oxidation (e.g., Cu(II)) of sulfhydryls or pesticide degradation, and released through sulfitolysis, metal-catalyzed thiol-disulfide exchange or related reactions; 3) S-alkylthioacetates, primarily formed during fermentation, and releasable hydrolytically. Some evidence also exists for S-amino acids serving as precursors. Based on these findings, we propose a “decision tree” approach to choosing appropriate strategies for managing wines with sulfurous off-aromas.