The development of computer fluid dynamics has been closely associated with the evolution of large high-speed computers. At first the principal incentive was to produce numerical techniques for solving problems related to national defense. Soon, however, it was recognized that numerous additional scientific and engineering applications could be accomplished by means of modified techniques that extended considerably the capabilities of the early procedures. This paper describes some of this work at The Los Alamos National Laboratory, where many types of problems were solved for the first time with the newly emerging sequence of numerical capabilities. The discussions focus principally on those with which the author has been directly involved.