Biogenically emitted dimethylsulfide (CH3-S-CH3, DMS) is the largest natural and second largest overall source of atmospheric sulfur. In the atmosphere DMS is oxidized by a complex mechanism to a variety of gaseous species, including H2SO4. Gas-phase sulfuric acid has an extremely low vapor pressure, and so it contributes to aerosol and, subsequently, cloud formation under special conditions. The DMS-aerosol-cloud link is complicated by the non-linearity of aerosol nucleation and the spatial disparity between high DMS concentrations, which occur near the surface, and low temperatures conducive to aerosol formation, which occur in the upper troposphere. Global distributions of gaseous H$_2$SO$_4$ are estimated from simulations of DMS chemistry using the 3D Model of Atmospheric Transport and Chemistry. The model contains the major DMS-related sources and sinks (oceanic emissions, wet and dry deposition, photochemical conversion, and scavenging by background aerosols). Uncertainties inherent in DMS oxidation are also considered by using two different chemical mechanisms (5-reaction parameterized and 46-reaction comprehensive schemes). For confidence, the modeled H2SO4 is compared with gas-phase measurements from ACE-1 and PEM Tropics-A. Along with temperature and relative humidity, the DMS-derived sulfuric acid is used to compute H2SO4-H2O binary nucleation (BN) rates throughout the troposphere. This analysis shows that DMS oxidation does not lead to appreciable aerosol formation through BN in most of the lower troposphere. More specifically, between 60$^\circ$S and 60$^\circ$N in the lowest 1 km both DMS mechanisms produce BN rates of less than 10$^{-5}$ particles cm$^{-3}$ s$^{-1}$. These low rates indicate that an additional process such as ternary nucleation is likely required to explain particle formation in the lower troposphere. In the upper troposphere the H$_2$SO$_4$ levels are low, yet sufficient enough to induce BN when combined with the cold upper tropospheric temperatures. Just below the tropical tropopause, both DMS mechanisms yield BN rates that exceed 1 particle cm$^{-3}$ s$^{-1}$. These large tropical upper tropospheric nucleation rates provide evidence that the DMS cycle may serve as an important source of natural aerosols to the lower stratosphere, which may have relevance to climate and the ozone layer.