Half-metallic magnetic materials are a new state of matter which is attracting more and more attention in recent years. With a special band structure in which only one of the two spin directions is metallic, the conducting electrons are completely spin polarized in these materials. This property makes it possible for them to play a key role in future electronic devices and to offer an interesting field for the study of spin-polarized transport theory and spin electronics. We review the history and properties of half-metallic magnets, as well as ongoing theoretical and experimental studies to find more evidence and examples of these materials. In addition, the magnetoresistance in half-metallic magnets is described in detail since this property has great importance in applications.