Viscosity of silicate melts is of fundamental importance in understanding volcanic and magmatic processes in Earth. In this dissertation, experiments were conducted to obtain high-pressure viscosity data in high viscosity range, and empirical models were constructed to predict viscosity of all natural silicate melts.A new empirical viscosity equation for natural anhydrous and hydrous silicate melts was developed, accounting for the dependence on temperature and melt composition (including water content). This equation with 37 fitted parameters can fit the entire high- and low-temperature viscosity database (1451 data points) of all ;;natural” silicate melts with 0.61 log units in terms of 2 deviation. This general model can be applied to calculate viscosity for modeling magma chamber processes and volcanic eruptions. It can also be used to estimate glass transition temperature and cooling rate of natural silicate melts.Because the pressure dependence of hydrous melt viscosity at low temperature is not known, new research was carried out to investigate the pressure effect on hydrous melt viscosity.First, the speciation of dissolved H2O in rhyolitic melts with 0.8 – 4 wt% water under pressure 0.94 – 2.83 GPa was determined.In addition to their importance in understanding hydrous melt structure, the data are critical for viscosity inference using a newly developed hydrous reaction viscometer.The new viscometry has been extended to hydrous rhyolitic melts with 0.8 - 4.0 wt% water for the first time in the high viscosity range and high pressure, up to 2.8 GPa. Besides this new method, a parallel plate viscometer in an internally-heated pressure vessel was used to measure the viscosity of rhyolitic melts containing 0.13 and 0.8 wt% water at 0.2 and 0.4 GPa. Combined with literature data, a model was developed to accommodate the effect of pressure, temperature and water content on the viscosity of rhyolitic melt. The results show the dependence of viscosity on pressure is complicated but relatively weak.