Boiling has been studied extensively during the last half of the 20th century. Many correlations and semimechanistic models have also been developed for various modes of boiling. However, due to the complexity involved in modeling continuously evolving vapor - liquid interfaces unrealistic assumptions are often made in developing various models. With the advances of recent years in the area of computational science and engineering, it is now, possible to solve, completely: the conservation equations of mass momentum, and energy for liquid and vapor phases simultaneously when an interface is continuously evolving at and near a heated surface. The solutions provide not only detailed physics of associated thermal and hydrodynamic processes, but also the shape of the evolving interface. In demonstrating the application of numerical simulations as an effective tool, both pool nucleate and film boiling at normal earth gravity and nucleate boiling under microgravity conditions are considered. Although these simulations have been computationally intensive in the future calculations of this type are expected to become routine.