In chemical and pharmaceutical industries, sulfur-containing compounds may exist in gas and liquid mixtures, and need to be removed. In this study, we report a molecular simulation study to investigate the adsorption and separation of t-butyl-mercaptan (TBM) in natural gas, as well as dimethyl sulfoxide (DMSO) in aqueous solution, by UiO-66 and its functional derivatives UiO-66-F-4, -(CH3)(2), -(COOH)(2), -(CF3)(2), and -naphthyl. It is revealed that the functional groups can act as additional adsorption sites and create stronger surface potential overlap, thus generally enhance adsorption capability. All the six UiO-66s show high adsorption capacity for TBM, except UiO-66- naphthyl due to reduced porosity and surface area. The TBM/CH4 selectivity is predicted to be high in these UiO-66s, ranging from 2.2 x 10(4) to 2.4 x 10(5); intriguingly, the TBM separation is not affected by the presence of trace H2O. The UiO-66s also exhibit good adsorption capacity and high selectivity for DMSO from aqueous solution, with DMSO/water selectivity up to 570 in UiO-66. This study provides microscopic insights into the selective adsorption of sulfur-containing compounds in both gas and liquid mixtures, and suggests that UiO-66s might be promising nanoporous materials for industry-relevant separation.