In this paper, the history of tropical cyclone modeling will be reviewed, with an emphasis on the Atlantic basin. According to Cressman (1996), routine operational numerical weather prediction in the U.S. officially began on May 6, 1955. These early predictions used a barotropic model to forecast the mid-atmospheric flow pattern over a limited region of North America. By the late 1950's, specialized barotropic models were developed for the prediction of tropical cyclone tracks. Research in the 1960's lead to the first successful axisymmetric models for the simulation of the life cyclone of tropical cyclones. By the 1970's, the research models were generalized to three dimensions, and the first operational three-dimensional hurricane model was implemented (the Moveable Fine Mesh model). By the 1980's computer power increased to the point where the resolution of global models was fine enough to resolve some aspects of tropical cyclones, and the global models eventually provided very accurate track forecasts. By the 1990's and 2000's, fully non-hydrostatic models were developed for research, and these will become the next generation operational forecast models. The past successes and future challenges in tropical cyclone modeling will be described.