The development of fluid mechanics is briefly reviewed, and the importance of fluid flows to heat and mass transport in nature and also in science and engineering is outlined. The early theoretical developments are explained, and it is indicated that the basic equations were already available at the end of the 18th century. Methods to solve these equations for engineering flows were not, however, developed until the second half of the 20th century. This was an important period for fluid flow research during which all the experimental fluid mechanics methods, particularly the optical methods, available today were also developed. The same is true for all the numerical methods that are used very successfully nowadays to solve scientific and engineering fluid flow problems. The Institute of Fluid Mechanics at the University of Erlangen-Nürnberg has contributed extensively to these developments.