In this dissertation, numerical methods useful for the simulation of gas-liquid multiphase flows are presented. Multiphase flows are commonly found throughout nature, human life, and engineering devices. As a result, accurate and predictive simulations of such flows will improve our understanding of these complex systems and aid in the development of more efficient engineering devices that exploit multiphase dynamics. The majority of multiphase flows dynamics occur at the gas-liquid interface. For example, many quantities (e.g., density and species concentrations) are discontinuous at the interface and surface tension is a singular force that acts at the interface. Therefore, accurately tracking the location of the interface, sharply handling discontinuities, and computing accurate interface curvature are critical components for predictive simulations of multiphase flows. In this work, two novel interface tracking strategies are proposed and tested. The methods extend the capabilities of both level set and volume-of-fluid (VOF) methods, which are commonly used interface capturing methodologies. A discretely consistent methodology is presented to transport VOF and additional quantities that may be discontinuous at the phase interface. By using the same transport scheme for the phase interface and the quantities, discrete conservation and second-order solution of the conservation laws is achieved. An improvement is proposed to the height function method, which is often used to compute the cur- vature in VOF simulations. Additionally, the height function method is extended to compute the curvature in the context of a conservative level set. These methods are used to simulate atomization, an important process in the combustion of liquid fuels. Namely, a liquid jet in cross-flow, an air-blast atomizer, and an electrically charged spray, are simulated and the results are compared to available experimental data. Qualitative comparisons of the spray appearance as well as quantitative measures of the spray penetration, drop size distributions, and droplet velocity distributions show that the simulations are capable of predicting the spray characteristics and are a viable tool in the engineering design process. Furthermore, the simulations provide a wealth of data that is useful for improving our understanding of multiphase flow systems.