The motion of fluids is a complex area of physics because of the non-linearity of their equations of motion. As an introduction to the field, a selection of important results in the motions of fluids and gases, illustrating the richness and complexity of the subject as well as the often non-intuitive features of fluid flow, are presented.The topics include Bernoulli’s equations, gravity waves in shallow and deep water, viscous flow, Stokes’ formula for viscous flow past a spherical body, vorticity and Kelvin’s circulation theorem. The emphasis is upon the physics of the problems, rather than the mathematical complexities involved.