Magnetic fluids may be classified as ferrofluids (FF), which are colloidal suspensions of very fine (∼ 10 nm) magnetic particles, and magnetorheological fluids, which are suspensions of larger, usually non-stable, magnetic particles. We review the general classification and the main properties of FF, some theoretical models and a few applications. We consider the stability of a FF in terms of various forces and torques on the magnetic particles. We discuss thermodiffusion, which is an important phenomenon in FF, and which gives rise to the Soret effect. We also consider the rotational dynamics of the magnetic moments of the particles. A large portion of this review is dedicated to applications of FF, including a few of the many technological applications. Among the uses of a FF in the study of materials, we have selected the doping of liquid crystals. Among the very promising uses in Medicine, we discuss drug targeting, hyperthermia, cell separation, and contrast in magnetic resonance imaging. We also make some comments on directions for future research on the properties of ferrofluids.