Computational Combustion or Numerical Simulations of Combustion can play an important role in the research and development of technologies to address sustainable energy, power, and propulsion. In this paper, the complexity of combustion and the challenges they pose in their numerical simulations are addressed first. Then, the role of computational combustion is examined in terms of the expected application which can range from “studies of fundamental issues” to “system-level performance estimates.” Of course, the same tool will not be necessary or practical to perform the various types of studies. Therefore, numerical simulations are classified into four levels or types: Detailed, Global, Specific System, and Idealized System Simulations. Each of these types is illustrated with examples with a discussion of their advantages and limitations.