In the past few decades, computational fluid dynamics modeling of fires has increased dramatically due in large part to the availability of powerful, reasonably priced computers. At NIST, a Large Eddy Simulation model called the Industrial Fire Simulator is being developed that exploits this power by emphasizing high spatial resolution and efficient flow solving techniques to predict the growth and spread of fire inside and outside of buildings. Great efficiency is obtained by discretizing the governing equations on rectilinear grids and forcing the geometry to conform to the grid. Because simulations involving several million grid cells are possible on modestly priced workstations and high-end personal computers, fairly elaborate geometries can be considered without sacrificing spatial resolution. An approximate form of the Navier-Stokes equations appropriate for low Mach number applications is used in the model. The approximation involves the filtering out of acoustic waves while allowing for large variations in temperature and density. Lagrangian particles or "thermal elements" are used to introduce the thermal energy of the fire into the calculation, and also to visualize the movement of the smoke and hot gases. The thermal elements carry the heat released by the fire, providing a self-consistent description of the smoke transport at all resolvable length and time scales. Large temperature and pressure variations are permitted, subject to the limitation that the Mach Number is about 0.3 or less. The methodology has been used to study a number of fire-related phenomena, for example, the interaction of draft curtains and sprinkler sprays, flows through vents, wind effects on buildings, large outdoor fires, and more basic combustion problems.